In 50 words or thereabout, How do you determine if a polynomial is the difference of two squares?
Q. Can you please explain this in laymen's terms? I am having a rough time understanding these concepts, definitions, and then the actual mathematical problems as well. Thanks so much!
Asked by Dedicated - Wed Nov 18 20:55:50 2009 - - 1 Answers - 0 Comments
A. If the first term and the second term are both squares, and they're separated by a - . eg. x2 - 25 a difference of squares. x2= X x X and 25= 5x5 to factor this it would break down into (x-5)(x+5) Be careful with differences such as... x4-81. This breaks down into (x2-9)(x2+9) then it needs to be further broken down as (x2-9) is also a difference of squares. The final answer for this factorization would be, (x2+9)(x-3)(x+3) The best way to determine whether or not a variable is a square is if it has an exponent of 2 or an exponent that is a multiple of 2. If you want to determine whether or not a number is a square, then use the square root function on your calculator and see if it works out to a whole number. As long as the first… [cont.]
Answered by violetraiyne - Wed Nov 18 21:10:41 2009
Q. Can you please explain this in laymen's terms? I am having a rough time understanding these concepts, definitions, and then the actual mathematical problems as well. Thanks so much!
Asked by Dedicated - Wed Nov 18 20:55:50 2009 - - 1 Answers - 0 Comments
A. If the first term and the second term are both squares, and they're separated by a - . eg. x2 - 25 a difference of squares. x2= X x X and 25= 5x5 to factor this it would break down into (x-5)(x+5) Be careful with differences such as... x4-81. This breaks down into (x2-9)(x2+9) then it needs to be further broken down as (x2-9) is also a difference of squares. The final answer for this factorization would be, (x2+9)(x-3)(x+3) The best way to determine whether or not a variable is a square is if it has an exponent of 2 or an exponent that is a multiple of 2. If you want to determine whether or not a number is a square, then use the square root function on your calculator and see if it works out to a whole number. As long as the first… [cont.]
Answered by violetraiyne - Wed Nov 18 21:10:41 2009
What is the difference between polynomials and two squares?
Q. How do you determine if a polynomial is the difference of two squares?
Asked by pinkroses_1983 - Thu Jul 23 01:30:19 2009 - - 1 Answers - 0 Comments
A. The difference of two squares is of the form a b . If a or b contain coefficients, they must be perfect squres. For example, x 4y is the difference of two squares since 4 is a perfect square, but x 4y is not since 3 is not a perfect square. I hope that addresses what you were wondering about. (The difference of two squares is a polynomial, just of a special type).
Answered by Polyhymnio - Thu Jul 23 01:44:02 2009
Q. How do you determine if a polynomial is the difference of two squares?
Asked by pinkroses_1983 - Thu Jul 23 01:30:19 2009 - - 1 Answers - 0 Comments
A. The difference of two squares is of the form a b . If a or b contain coefficients, they must be perfect squres. For example, x 4y is the difference of two squares since 4 is a perfect square, but x 4y is not since 3 is not a perfect square. I hope that addresses what you were wondering about. (The difference of two squares is a polynomial, just of a special type).
Answered by Polyhymnio - Thu Jul 23 01:44:02 2009
How do you determine if a polynomial is the differences of two squares I need this is in 50 words?
Q. How do you determine if a polynomial is the differences of two squares I need this is in 50 words?
Asked by inlove_83 - Thu Sep 2 10:35:34 2010 - - 3 Answers - 0 Comments
Q. How do you determine if a polynomial is the differences of two squares I need this is in 50 words?
Asked by inlove_83 - Thu Sep 2 10:35:34 2010 - - 3 Answers - 0 Comments
How do you determine if a polynomial?
Q. How do you determine if a polynomial is the difference of two squares?
Asked by tasheeepoo - Wed Aug 12 01:22:51 2009 - - 1 Answers - 0 Comments
A. If you allow square roots, any two term expression with a minus sign inbetween can be written as a difference of squares: 2 - 3x = ( 2 - (3x)) ( 2 + (3x)) 5 - 9x^4 z^2 = ( 5 - 3x^2 z) ( 5 + 3x^2 z) If you aren't supposed to have radicals, you'll need the coefficients to be squares and all the variable exponents to be even: 49 x^6 - 81 y^4 z^2 = (7 x^3 - 9 y^2 z) (7 x^3 + 9 y^2 z) Actually, if you can have imaginary numbers, you can even treat things like 4 + 9x^2 as a difference of squares, but I'm guessing that isn't fair game for you.
Answered by brashion - Wed Aug 12 01:55:37 2009
Q. How do you determine if a polynomial is the difference of two squares?
Asked by tasheeepoo - Wed Aug 12 01:22:51 2009 - - 1 Answers - 0 Comments
A. If you allow square roots, any two term expression with a minus sign inbetween can be written as a difference of squares: 2 - 3x = ( 2 - (3x)) ( 2 + (3x)) 5 - 9x^4 z^2 = ( 5 - 3x^2 z) ( 5 + 3x^2 z) If you aren't supposed to have radicals, you'll need the coefficients to be squares and all the variable exponents to be even: 49 x^6 - 81 y^4 z^2 = (7 x^3 - 9 y^2 z) (7 x^3 + 9 y^2 z) Actually, if you can have imaginary numbers, you can even treat things like 4 + 9x^2 as a difference of squares, but I'm guessing that isn't fair game for you.
Answered by brashion - Wed Aug 12 01:55:37 2009
help with this math question..?
Q. How do you determine if a polynomial is the difference of two squares? (50 or more words)
Asked by Tina - Tue Jun 15 15:18:34 2010 - - 1 Answers - 0 Comments
A. observe the following problem: (x - 2)(x + 2) x2 + 2x - 2x - 4 x2 - 4 In this case, the multiplication of the outer terms and of the inner terms resulted in 2x and -2x. The terms 2x and -2x have coefficients of 2 and -2. These coefficients are essentially the same number, but with with opposite signs (one number is positive and the other is negative). These two terms form a zero pair, meaning when they are combined, they cancel each other out. You can see that in the last step of the problem, where like terms were combined, the zero pair 2x and -2x canceled out. As a result, only two terms remained on the last line. The result from the last problem is called a Difference Between Two Squares. A Difference Between Two Squares is… [cont.]
Answered by greg h - Tue Jun 15 15:28:43 2010
Q. How do you determine if a polynomial is the difference of two squares? (50 or more words)
Asked by Tina - Tue Jun 15 15:18:34 2010 - - 1 Answers - 0 Comments
A. observe the following problem: (x - 2)(x + 2) x2 + 2x - 2x - 4 x2 - 4 In this case, the multiplication of the outer terms and of the inner terms resulted in 2x and -2x. The terms 2x and -2x have coefficients of 2 and -2. These coefficients are essentially the same number, but with with opposite signs (one number is positive and the other is negative). These two terms form a zero pair, meaning when they are combined, they cancel each other out. You can see that in the last step of the problem, where like terms were combined, the zero pair 2x and -2x canceled out. As a result, only two terms remained on the last line. The result from the last problem is called a Difference Between Two Squares. A Difference Between Two Squares is… [cont.]
Answered by greg h - Tue Jun 15 15:28:43 2010
Omg Someone help Math Test tomorrow and i cant even do this stupid review!
Q. Someone please help me with this review??? 1. Use three or more sentences to describe how you identify whether or not a polynomial is a difference of two squares. Then, factor the polynomial 4x^2-36. 2. Use three or more sentences to describe how you identify whether or not a polynomial is a perfect square trinomial. Then, factor the polynomial x^2-40x 400. 3. Consider the factoring process that has been illustrated below. Use three or more sentences to describe the process used to factor this polynomial. 3y^3 4y^2-12y-16 =y^2(3y 4)-4(3y 4) =(3y 4)(y2-4) =(3y 4)(y 2)(y-2) 4. Use three or more sentences to describe the process you would follow to completely factor the polynomial 3x^6 24. 5. Honors Only: Look at the equation y10^n -… [cont.]
Asked by Pappas07 - Fri Aug 8 23:25:43 2008 - - 2 Answers - 0 Comments
A. 1. 4x - 36 4(x - 9) 4(x+3)(x-3) Practice 3x - 12 2x - 32 2. x - 40x +400 (x-20)(x-20) Practice x - 30x + 900 x - 6x + 9 x + 4x + 4 3. 3x^6 +24 3(x^6 + 8) 3(x +2)(x^4 + 2x + 4) Practice 4x^12 +32 5. y^10n - 2y^5n + 1 Perfect square trinomial First term is a perfect square Last term is a perfect square middle term is 2*square root of first term*square root of last term (y^5n - 1)(y^5n- 1)
Answered by AC - Fri Aug 8 23:38:26 2008
Q. Someone please help me with this review??? 1. Use three or more sentences to describe how you identify whether or not a polynomial is a difference of two squares. Then, factor the polynomial 4x^2-36. 2. Use three or more sentences to describe how you identify whether or not a polynomial is a perfect square trinomial. Then, factor the polynomial x^2-40x 400. 3. Consider the factoring process that has been illustrated below. Use three or more sentences to describe the process used to factor this polynomial. 3y^3 4y^2-12y-16 =y^2(3y 4)-4(3y 4) =(3y 4)(y2-4) =(3y 4)(y 2)(y-2) 4. Use three or more sentences to describe the process you would follow to completely factor the polynomial 3x^6 24. 5. Honors Only: Look at the equation y10^n -… [cont.]
Asked by Pappas07 - Fri Aug 8 23:25:43 2008 - - 2 Answers - 0 Comments
A. 1. 4x - 36 4(x - 9) 4(x+3)(x-3) Practice 3x - 12 2x - 32 2. x - 40x +400 (x-20)(x-20) Practice x - 30x + 900 x - 6x + 9 x + 4x + 4 3. 3x^6 +24 3(x^6 + 8) 3(x +2)(x^4 + 2x + 4) Practice 4x^12 +32 5. y^10n - 2y^5n + 1 Perfect square trinomial First term is a perfect square Last term is a perfect square middle term is 2*square root of first term*square root of last term (y^5n - 1)(y^5n- 1)
Answered by AC - Fri Aug 8 23:38:26 2008
How do you determine if a polynomial is the difference of two squares?
Q. Really am having a problem with this!
Asked by Heidi - Mon Mar 8 12:23:13 2010 - - 4 Answers - 0 Comments
A. There have to be two terms. The operation between the two terms is subtraction. Each term (after removing any common factors) is a perfect square. Seems pretty straightforward ! Think ! Practice.
Answered by the mathemagician - Mon Mar 8 12:27:12 2010
Q. Really am having a problem with this!
Asked by Heidi - Mon Mar 8 12:23:13 2010 - - 4 Answers - 0 Comments
A. There have to be two terms. The operation between the two terms is subtraction. Each term (after removing any common factors) is a perfect square. Seems pretty straightforward ! Think ! Practice.
Answered by the mathemagician - Mon Mar 8 12:27:12 2010
How do you determine if a polynomial is the difference of two squares?
Q. Aim for a 50 word detailed response please. Thanks!
Asked by Dedicated - Wed Nov 18 01:39:29 2009 - - 1 Answers - 0 Comments
A. x^2 - 4 = (x+2)(x-2) x^2 - 9 = (x+3)(x-3) x^2 - 16 = (x+4)(x-4) x^2 - 25 = (x+5)(x-5) x^2 - 36 = (x+6)(x-6) x^2 - 49 = (x+7)(x-7) x^2 - 64 = (x+8)(x-8) x^2 - 81 = (x+9)(x-9) x^2 - 100 = (x+10)(x-10) etc. if you see that (it has to be subtracting, not adding) where x squared is subtracting a square, hence the difference of two squares, then you know.
Answered by Geoffrey T - Wed Nov 18 01:44:10 2009
Q. Aim for a 50 word detailed response please. Thanks!
Asked by Dedicated - Wed Nov 18 01:39:29 2009 - - 1 Answers - 0 Comments
A. x^2 - 4 = (x+2)(x-2) x^2 - 9 = (x+3)(x-3) x^2 - 16 = (x+4)(x-4) x^2 - 25 = (x+5)(x-5) x^2 - 36 = (x+6)(x-6) x^2 - 49 = (x+7)(x-7) x^2 - 64 = (x+8)(x-8) x^2 - 81 = (x+9)(x-9) x^2 - 100 = (x+10)(x-10) etc. if you see that (it has to be subtracting, not adding) where x squared is subtracting a square, hence the difference of two squares, then you know.
Answered by Geoffrey T - Wed Nov 18 01:44:10 2009
How do you determine if a polynomial is the difference of two squares?
Q. How do you determine if a polynomial is the difference of two squares?
Asked by Naty p - Thu Mar 13 22:43:50 2008 - - 2 Answers - 0 Comments
A. Only one term can be negative of the binomial x^2 - y^2 -x^2 + y^2 which would be rewritten as y^2 - x^2 the powers on all variables must be even x^2 x^4= (x^2)^2 x^6=( x^3)^2 etc the number coefficients must be perfect squares 1,4,9,16,25,36,49,... or any fraction combination of these: 1/16 or 49/81 for example. Also decimals: 0.04, 0.25, ... You can always check on a calculator to see if the square root of the number gives you a "perfect answer" Hope that helps!
Answered by A b z m b i - Thu Mar 13 22:48:15 2008
Q. How do you determine if a polynomial is the difference of two squares?
Asked by Naty p - Thu Mar 13 22:43:50 2008 - - 2 Answers - 0 Comments
A. Only one term can be negative of the binomial x^2 - y^2 -x^2 + y^2 which would be rewritten as y^2 - x^2 the powers on all variables must be even x^2 x^4= (x^2)^2 x^6=( x^3)^2 etc the number coefficients must be perfect squares 1,4,9,16,25,36,49,... or any fraction combination of these: 1/16 or 49/81 for example. Also decimals: 0.04, 0.25, ... You can always check on a calculator to see if the square root of the number gives you a "perfect answer" Hope that helps!
Answered by A b z m b i - Thu Mar 13 22:48:15 2008
How do you determine if a polynomial is the difference of two squares?
Q. How do you determine if a polynomial is the difference of two squares?
Asked by mj - Fri May 23 14:04:59 2008 - - 4 Answers - 0 Comments
A. There are three interpretations to this, because the statement is ambiguous. Polynomials are constructed from variables and coefficients. They may nor may not have a constant term. We consider polynomials with integer coefficients, i.e. of the form &sum(i=0, n, k sub i * a^i) 1. The polynomial reduces to an integer which is the difference of two squares. In this case, you have to make sure that 1) the polynomial reduces after simplification to its constant term; and 2) that that constant term is an integer and can be expressed as the difference of two integer squares, i.e. of the form n - m². Since n - is equal to (n+m)(n-m) it suffices to find whether the constant term admits a factorization of this form (cf below). 2. The… [cont.]
Answered by Bazz - Fri May 23 17:23:21 2008
Q. How do you determine if a polynomial is the difference of two squares?
Asked by mj - Fri May 23 14:04:59 2008 - - 4 Answers - 0 Comments
A. There are three interpretations to this, because the statement is ambiguous. Polynomials are constructed from variables and coefficients. They may nor may not have a constant term. We consider polynomials with integer coefficients, i.e. of the form &sum(i=0, n, k sub i * a^i) 1. The polynomial reduces to an integer which is the difference of two squares. In this case, you have to make sure that 1) the polynomial reduces after simplification to its constant term; and 2) that that constant term is an integer and can be expressed as the difference of two integer squares, i.e. of the form n - m². Since n - is equal to (n+m)(n-m) it suffices to find whether the constant term admits a factorization of this form (cf below). 2. The… [cont.]
Answered by Bazz - Fri May 23 17:23:21 2008
How do you determine if a polynomial is the difference of two squares?
Q. in words please
Asked by mamichula174 - Fri Jun 12 20:30:50 2009 - - 2 Answers - 0 Comments
Q. in words please
Asked by mamichula174 - Fri Jun 12 20:30:50 2009 - - 2 Answers - 0 Comments
how do you determine if a polynomial is the difference of two squares?
Q. how do you determine if a polynomial is the difference of two squares?
Asked by ms_werts - Thu Jan 15 22:03:38 2009 - - 1 Answers - 0 Comments
A. I believe that specifically the polynomial in question must be a binomial, (two terms only) but it's fairly straight forward something like x^2-9 is a difference of square because x^2 is the result of x*x and 9 can be interpreted as the result of 3*3 it's a pretty mentally based process but if you wanted a concrete rule you could take the square root of each term in the binomial and if it comes out perfectly, you have a difference of squares
Answered by patrick - Thu Jan 15 22:12:32 2009
Q. how do you determine if a polynomial is the difference of two squares?
Asked by ms_werts - Thu Jan 15 22:03:38 2009 - - 1 Answers - 0 Comments
A. I believe that specifically the polynomial in question must be a binomial, (two terms only) but it's fairly straight forward something like x^2-9 is a difference of square because x^2 is the result of x*x and 9 can be interpreted as the result of 3*3 it's a pretty mentally based process but if you wanted a concrete rule you could take the square root of each term in the binomial and if it comes out perfectly, you have a difference of squares
Answered by patrick - Thu Jan 15 22:12:32 2009
In 50 words or thereabout, How do you determine if a polynomial is the difference of two squares?
Q. In 50 words or thereabout, How do you determine if a polynomial is the difference of two squares?
Asked by Dedicated - Wed Nov 18 19:27:43 2009 - - 1 Answers - 0 Comments
A. the sign of the polynomial is -. the two terms are perfect squares. ex: x^2-25= [x+5][x-5] x^4 -49= [x^2+7][x^2-7] x^16-100= [x^4+10][x^4-10] x^2 - 81= [x-9][x+9] it can NEVER be: x^2+25, x^2+49, x^4+36 because the sign in the middle must be [ - ]
Answered by LizardLover - Wed Nov 18 19:33:05 2009
Q. In 50 words or thereabout, How do you determine if a polynomial is the difference of two squares?
Asked by Dedicated - Wed Nov 18 19:27:43 2009 - - 1 Answers - 0 Comments
A. the sign of the polynomial is -. the two terms are perfect squares. ex: x^2-25= [x+5][x-5] x^4 -49= [x^2+7][x^2-7] x^16-100= [x^4+10][x^4-10] x^2 - 81= [x-9][x+9] it can NEVER be: x^2+25, x^2+49, x^4+36 because the sign in the middle must be [ - ]
Answered by LizardLover - Wed Nov 18 19:33:05 2009
How do you determine if a polynomial is the difference of two squares?
Q. I totally don't get this.
Asked by Sam - Fri Jan 22 17:56:27 2010 - - 6 Answers - 0 Comments
A. The two terms are separated by a negative sign. Both terms must be perfect squares. That means the coefficient, if one exists, as well as the variable. They will have the basic look of: (A^2 - B^2) which becomes (A + B)(A - B). So, for example, if you have 9x^4 - 25y^2: 9x^4 is a perfect square meaning you can take the square root of it. 9x^4 = 3x^2 times 3x^2. 9x^4 is A^2. Also, 25y^2 is a perfect square. The square root is 5y. 5y times 5y = 25y^2. 25y^2 is B^2. So 9x^4 - 25^2 = (3x^2 + 5y)(3x^2 - 5y). Hope this makes sense to you. It is easier to explain in spoken word than by keyboarding.
Answered by czar - Fri Jan 22 18:07:22 2010
Q. I totally don't get this.
Asked by Sam - Fri Jan 22 17:56:27 2010 - - 6 Answers - 0 Comments
A. The two terms are separated by a negative sign. Both terms must be perfect squares. That means the coefficient, if one exists, as well as the variable. They will have the basic look of: (A^2 - B^2) which becomes (A + B)(A - B). So, for example, if you have 9x^4 - 25y^2: 9x^4 is a perfect square meaning you can take the square root of it. 9x^4 = 3x^2 times 3x^2. 9x^4 is A^2. Also, 25y^2 is a perfect square. The square root is 5y. 5y times 5y = 25y^2. 25y^2 is B^2. So 9x^4 - 25^2 = (3x^2 + 5y)(3x^2 - 5y). Hope this makes sense to you. It is easier to explain in spoken word than by keyboarding.
Answered by czar - Fri Jan 22 18:07:22 2010
How do you determine if a polynomial is the difference of two squares?
Q. How do you determine if a polynomial is the difference of two squares?
Asked by LowProC - Wed Apr 23 22:54:39 2008 - - 4 Answers - 0 Comments
A. Every polynomial is the difference of two squares, since (p/4+1)^2 - (p/4-1)^2 = p.
Answered by Low Key Lyesmith - Wed Apr 23 23:21:59 2008
Q. How do you determine if a polynomial is the difference of two squares?
Asked by LowProC - Wed Apr 23 22:54:39 2008 - - 4 Answers - 0 Comments
A. Every polynomial is the difference of two squares, since (p/4+1)^2 - (p/4-1)^2 = p.
Answered by Low Key Lyesmith - Wed Apr 23 23:21:59 2008
How do you determine if a polynomial is the difference of two squares?
Q. How do you determine if a polynomial is the difference of two squares?
Asked by MiMi - Fri Aug 3 13:07:55 2007 - - 2 Answers - 0 Comments
A. The difference of two square quadratics follows the form below: a^2 - b^2 = (a-b) (a+b) So, if a polynomial can be re-arranged to the format below: (a-b) (a+b) then that polynomial is the difference of 2 squares. For example, this polynomial ( 5x + 10y) (5x - 10y) is the difference of 2 squares, because it follows the formula (a+b) (a-b) where a = 5x, and b = 10y so, (5x +10y) (5x -10y) = (5x)^2 - (10y)^2 = 25x^2 - 100y^2 Another example: 4ab is a difference of 2 squares because 4ab = 2ab + 2ab + (a^2 - a^2) + (b^2 - b^2) 4ab = (a^2 + 2ab + b^2) - (a^2 -2ab + b^2) 4ab = (a+b)^2 - (a-b)^2 where A = a+b, and B = a-b
Answered by buoisang - Fri Aug 3 13:52:10 2007
Q. How do you determine if a polynomial is the difference of two squares?
Asked by MiMi - Fri Aug 3 13:07:55 2007 - - 2 Answers - 0 Comments
A. The difference of two square quadratics follows the form below: a^2 - b^2 = (a-b) (a+b) So, if a polynomial can be re-arranged to the format below: (a-b) (a+b) then that polynomial is the difference of 2 squares. For example, this polynomial ( 5x + 10y) (5x - 10y) is the difference of 2 squares, because it follows the formula (a+b) (a-b) where a = 5x, and b = 10y so, (5x +10y) (5x -10y) = (5x)^2 - (10y)^2 = 25x^2 - 100y^2 Another example: 4ab is a difference of 2 squares because 4ab = 2ab + 2ab + (a^2 - a^2) + (b^2 - b^2) 4ab = (a^2 + 2ab + b^2) - (a^2 -2ab + b^2) 4ab = (a+b)^2 - (a-b)^2 where A = a+b, and B = a-b
Answered by buoisang - Fri Aug 3 13:52:10 2007
How do you determine if a polynomial is the difference of two squares?
Q. How do you determine if a polynomial is the difference of two squares?
Asked by icecrystal - Wed Jun 4 16:37:41 2008 - - 5 Answers - 0 Comments
A. difference of squares are x -y 4w -16p all terms must be square and there must be a negative sign in the middle This tells you if they are perfect squares 4x + 12x +9 = (2x+3) look at the problem take the sq rt or the first number and the third number mul them together double the answer if it equals the middle term it is a perfect square. 2(3) =6 2(6)=12 the middle number hope this helps!!!
Answered by Mich - Wed Jun 4 16:43:01 2008
Q. How do you determine if a polynomial is the difference of two squares?
Asked by icecrystal - Wed Jun 4 16:37:41 2008 - - 5 Answers - 0 Comments
A. difference of squares are x -y 4w -16p all terms must be square and there must be a negative sign in the middle This tells you if they are perfect squares 4x + 12x +9 = (2x+3) look at the problem take the sq rt or the first number and the third number mul them together double the answer if it equals the middle term it is a perfect square. 2(3) =6 2(6)=12 the middle number hope this helps!!!
Answered by Mich - Wed Jun 4 16:43:01 2008
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