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2006-12-24 10:36:00 · 8 answers · asked by Anonymous in Science & Mathematics Mathematics

8 answers

4x^2 - (x+y)^2
=(2x +x+y)(2x-x-y)
=(3x+y)(x-y)

2006-12-24 10:43:08 · answer #1 · answered by sahsjing 7 · 3 0

Your problem asked you to factor 2x² - 4x Your book got this answer: 2x ( x - 2 ) Here's how it got that answer: 1) First realize that 2x ² means that there are TWO x's in this term. You can write 2x² like this: 2xx <-- same as 2x² 2) So now you can see that each of the two terms has one factor in common -- namely 2x 3) So you divide each term by 2x to see how much will be left inside the parentheses after you divide out the common factor of 2x from each one 4) First you divide 2xx by 2x The "2" comes out, and one of the "x's" comes out, leaving one x inside 5) Then you divide the second term (which is 4x) also by the same 2x you used for the first term The solution for 4x/2x is 2 6) So you have this two-step problem: 2xx/2x (which equals x) and 4x/2x (which comes out to 2) 7) So you write the common factor of 2x on the outside of the parentheses 2x (.........) 8) and inside you write whatever was left after you divided out the 2x 2x ( x - 2 ) The key is seeing that 2x ² is not 2x. It is 2xx because the "squared" means that you have to multiply x times another x.

2016-05-23 04:37:52 · answer #2 · answered by ? 4 · 0 0

4x^2-(x+y)^2

=(2x)^2-(x+y)^2

This is the difference of squares
a^2-b^2=(a+b)(a-b)

In this case, a=2x and b=x+y

So we get (2x +(x+y)) (2x-(x+y))

(2x+x+y) (2x-x-y) by removing parenthesis and distributing the negative

(3x+y)(x-y)

2006-12-24 11:02:22 · answer #3 · answered by Professor Maddie 4 · 5 0

4x^2 - (x + y)^2
(2x - (x + y))(2x + (x + y))
(2x - x - y)(2x + x + y)
(x - y)(3x + y)

2006-12-25 02:31:24 · answer #4 · answered by Sherman81 6 · 0 0

4x^2-(x+y)^2
= (2x)^2-(x+y)^2
= [2x+(x+y)][2x-(x+y)]
= (2x+x+y)(2x-x-y)
= (3x+y)(x-y)

2006-12-24 10:46:04 · answer #5 · answered by kingbodonti 6 · 5 0

4x^2 - (x+y)^2
4x^2 - x^2 + 2xy + y^2
3x^2 + 2xy + y^2
x(3x + 2y) + y^2

2006-12-24 10:41:40 · answer #6 · answered by PIPI B 4 · 0 6

4x^2-(x+y)^2
4x^2-((x+y)(x+y))
4x^2-(x^2+2xy+y^2)
4x^2-x^2-2xy-y^2
3x^2-2xy-y^2
(3x+y)(x-y)

2006-12-24 11:45:34 · answer #7 · answered by Anonymous · 2 0

4x^2-x^2-2xy-y^2

3x^2-2xy-y^2

2006-12-24 10:43:37 · answer #8 · answered by abcde12345 4 · 0 4

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