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
In Algebra, how do you determine if a polynomial is the difference of two squares?
Q. In Algebra, how do you determine if a polynomial is the difference of two squares?
Asked by jmwills74@yahoo.com - Fri Mar 28 17:11:19 2008 - - 3 Answers - 0 Comments
A. Lots of polynomials can be the difference between to squares, but it doesnt mean you'd want to consider it so Just 4 examples Simple: a^2-b^2=(a-b)(a+b) x^2-4 = (x+4)(x-4) or harder x^2-2 = (x-sqrt2)(x+sqrt2) X^4-16 = (x^2-4)(x^2+4) remember differnece means minus difference of 2 squares means one square minus another but since x=sqtr(x)^2 you can treat any number as a square
Answered by Scrander berry - Fri Mar 28 17:21:28 2008
Q. In Algebra, how do you determine if a polynomial is the difference of two squares?
Asked by jmwills74@yahoo.com - Fri Mar 28 17:11:19 2008 - - 3 Answers - 0 Comments
A. Lots of polynomials can be the difference between to squares, but it doesnt mean you'd want to consider it so Just 4 examples Simple: a^2-b^2=(a-b)(a+b) x^2-4 = (x+4)(x-4) or harder x^2-2 = (x-sqrt2)(x+sqrt2) X^4-16 = (x^2-4)(x^2+4) remember differnece means minus difference of 2 squares means one square minus another but since x=sqtr(x)^2 you can treat any number as a square
Answered by Scrander berry - Fri Mar 28 17:21:28 2008
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
Polynomial question?
Q. How do you determine if a polynomial is the difference of two squares?
Asked by peaches - Mon Jan 14 19:31:01 2008 - - 3 Answers - 0 Comments
A. It'll be in the form a^2 - b^2. In other words, the first part will be a perfect square, and will so will the second. Examples of difference of two squares: 64 - x^4 = (8-y^2)(8+y^2) 16 - p^2 = (4-p)(4+p).
Answered by omgimagenius - Mon Jan 14 19:36:09 2008
Q. How do you determine if a polynomial is the difference of two squares?
Asked by peaches - Mon Jan 14 19:31:01 2008 - - 3 Answers - 0 Comments
A. It'll be in the form a^2 - b^2. In other words, the first part will be a perfect square, and will so will the second. Examples of difference of two squares: 64 - x^4 = (8-y^2)(8+y^2) 16 - p^2 = (4-p)(4+p).
Answered by omgimagenius - Mon Jan 14 19:36:09 2008
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. Can somebody help me?
Asked by Jessica - Fri Feb 26 22:46:20 2010 - - 3 Answers - 0 Comments
A. First of all, there are two terms. x^2 - y^2 is the difference of two squares. x is squared and so is y. The second thing is that they both have to be perfect squares or be able to be made so. 169x^2 - 25y^2 The square root of 169x^2 = 13x square root of 25y^2 = 5y. You can make it into a perfect square root by taking out a common factor. 50zx^2 - 162zy^2 Take out 2z from each term. 2z(25x^2 - 81y^2) = 2z is the common factor that can be taken from either side of the minus. 25x^2 's root is 5x 81y^2's root is 9y
Answered by jcherry_99 - Fri Feb 26 22:55:26 2010
Q. Can somebody help me?
Asked by Jessica - Fri Feb 26 22:46:20 2010 - - 3 Answers - 0 Comments
A. First of all, there are two terms. x^2 - y^2 is the difference of two squares. x is squared and so is y. The second thing is that they both have to be perfect squares or be able to be made so. 169x^2 - 25y^2 The square root of 169x^2 = 13x square root of 25y^2 = 5y. You can make it into a perfect square root by taking out a common factor. 50zx^2 - 162zy^2 Take out 2z from each term. 2z(25x^2 - 81y^2) = 2z is the common factor that can be taken from either side of the minus. 25x^2 's root is 5x 81y^2's root is 9y
Answered by jcherry_99 - Fri Feb 26 22:55:26 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 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 youravonwoman - Fri Oct 30 17:05:26 2009 - - 1 Answers - 0 Comments
A. It first has to be a bionomial, meaning there are two parts. Then, there needs to be a subtraction sign betweeen the two numbers for factoring to work. Finally, you have to make sure both have perfect square roots. For example, x^2 -144 Both x^2 and 144 are perfect squares, so you can detirmnie that it can be factored as: (x + 12)(x - 12)
Answered by Meghan - Fri Oct 30 17:24:18 2009
Q. How do you determine if a polynomial is the difference of two squares?
Asked by youravonwoman - Fri Oct 30 17:05:26 2009 - - 1 Answers - 0 Comments
A. It first has to be a bionomial, meaning there are two parts. Then, there needs to be a subtraction sign betweeen the two numbers for factoring to work. Finally, you have to make sure both have perfect square roots. For example, x^2 -144 Both x^2 and 144 are perfect squares, so you can detirmnie that it can be factored as: (x + 12)(x - 12)
Answered by Meghan - Fri Oct 30 17:24:18 2009
How do you determine if a polynomial is the difference of two squares?
Q. Please help
Asked by TJS Mom - Fri Aug 7 23:30:48 2009 - - 6 Answers - 0 Comments
A. Not always easy. For example 10x^2 + 5 is the difference of two squares. If you don't believe me, calculate this: (x^2+3)^2 - (x^2-2)^2 If you did it correctly you will get, after simplification, 10x^2 + 5.
Answered by JB - Fri Aug 7 23:39:36 2009
Q. Please help
Asked by TJS Mom - Fri Aug 7 23:30:48 2009 - - 6 Answers - 0 Comments
A. Not always easy. For example 10x^2 + 5 is the difference of two squares. If you don't believe me, calculate this: (x^2+3)^2 - (x^2-2)^2 If you did it correctly you will get, after simplification, 10x^2 + 5.
Answered by JB - Fri Aug 7 23:39:36 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 nayner06 - Fri Oct 9 10:49:24 2009 - - 2 Answers - 0 Comments
A. You look. You see two squares and a minus sign between them. The other tipoff is that there are two terms, not three. Sometimes you need to factor out common factors before you can see it. Example. 5x 20. 5 is not a sqaure; neither is 20. BUT you can factor out a 5. 5(x 4) Aha! 4 is 2 Always factor out any commons factors first thing.
Answered by Mark - Fri Oct 9 10:55:57 2009
Q. How do you determine if a polynomial is the difference of two squares?
Asked by nayner06 - Fri Oct 9 10:49:24 2009 - - 2 Answers - 0 Comments
A. You look. You see two squares and a minus sign between them. The other tipoff is that there are two terms, not three. Sometimes you need to factor out common factors before you can see it. Example. 5x 20. 5 is not a sqaure; neither is 20. BUT you can factor out a 5. 5(x 4) Aha! 4 is 2 Always factor out any commons factors first thing.
Answered by Mark - Fri Oct 9 10:55:57 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 Dedicated - Thu Nov 19 21:00:25 2009 - - 5 Answers - 0 Comments
A. If you are factoring, a difference of squares will have 2 terms. It looks like this: a^2 - b^2; and like this when fully factored: (a-b)(a+b). It can be recognized in these two steps: 1) It will have 2 terms, both perfect squares (Perfect square example: 16x^2). 2) There will be a minus sign between the two terms. For example: 25x^2 - 16, and will be (5x - 4)(5x + 4) when factored. Hope this helps.
Answered by Joseph B - Thu Nov 19 21:10:26 2009
Q. How do you determine if a polynomial is the difference of two squares?
Asked by Dedicated - Thu Nov 19 21:00:25 2009 - - 5 Answers - 0 Comments
A. If you are factoring, a difference of squares will have 2 terms. It looks like this: a^2 - b^2; and like this when fully factored: (a-b)(a+b). It can be recognized in these two steps: 1) It will have 2 terms, both perfect squares (Perfect square example: 16x^2). 2) There will be a minus sign between the two terms. For example: 25x^2 - 16, and will be (5x - 4)(5x + 4) when factored. Hope this helps.
Answered by Joseph B - Thu Nov 19 21:10:26 2009
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 greek10150 - Thu Oct 16 18:58:16 2008 - - 2 Answers - 0 Comments
A. If both terms are perfect squares, coefficients and variables. (4x - 9) is the difference of two squares, because 4, x , and 9 are all perfect squares. (400x^4y^8 - 1600x^8y^4) is the difference of two squares, because 400, x^4, y^8, 1600, x^8, and y^4 are all perfect squares. (2x - 1) is not the difference of two squares because 2 is not a perfect square. (3x - 12x) IS the difference of two squares...once you factor out the 3x, giving you 3x(x - 4), so you could factor (x - 4).
Answered by Elmyr - Thu Oct 16 19:12:13 2008
Q. How do you determine if a polynomial is the difference of two squares.?
Asked by greek10150 - Thu Oct 16 18:58:16 2008 - - 2 Answers - 0 Comments
A. If both terms are perfect squares, coefficients and variables. (4x - 9) is the difference of two squares, because 4, x , and 9 are all perfect squares. (400x^4y^8 - 1600x^8y^4) is the difference of two squares, because 400, x^4, y^8, 1600, x^8, and y^4 are all perfect squares. (2x - 1) is not the difference of two squares because 2 is not a perfect square. (3x - 12x) IS the difference of two squares...once you factor out the 3x, giving you 3x(x - 4), so you could factor (x - 4).
Answered by Elmyr - Thu Oct 16 19:12:13 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 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
From Yahoo Answer Search: 'How do you determine if a polynomial is the difference of two squares?'
Tue Mar 9 17:10:51 2010 [ refresh local cache ]
