# [Factorization] Factorization of Square factors

• Mar 4th 2010, 01:29 AM
Cthul
[Factorization] Factorization of Square factors
How do I factorize (further) this? I do not understand the steps, I know the answer although.

The question goes:

1)
(x-b)^2-x+b

=(x-b)^2-(x-b)
=(x-b)(x-b-1)

I do not understand the steps from 2nd to 3rd.

2)
x^2-y^2-(x-y)^2

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

I do not get the step from 1 to 2.

Explanation would be appreciated.
• Mar 4th 2010, 01:40 AM
u2_wa
Quote:

Originally Posted by Cthul
How do I factorize (further) this? I do not understand the steps, I know the answer although.

The question goes:

1)
(x-b)^2-x+b

=(x-b)^2-(x-b)
=(x-b)(x-b-1)

I do not understand the steps from 2nd to 3rd.

Explanation would be appreciated.

Suppose the equation is as such: \$\displaystyle a^2-a\$
To simplify it take \$\displaystyle a\$ common i.e \$\displaystyle a(a-1)\$

In the same way take \$\displaystyle (x-b)\$ common from \$\displaystyle (x-b)^2-(x-b)\$ i.e
\$\displaystyle (x-b)[(x-b)-1]\$.

You could also do it by substituting \$\displaystyle a\$ with \$\displaystyle (x-b)\$ in equation \$\displaystyle a(a-1)=(x-b)[(x-b)-1]\$

Hope this helps!!!
• Mar 4th 2010, 01:49 AM
u2_wa
Quote:

Originally Posted by Cthul
How do I factorize (further) this? I do not understand the steps, I know the answer although.

2)
x^2-y^2-(x-y)^2

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

I do not get the step from 1 to 2.

Explanation would be appreciated.

Do you know this identity \$\displaystyle (a+b)(a-b)=a^2-b^2\$

To solve this equation :\$\displaystyle \color{red}x^2-y^2\color{black}-(x-y)^2\$

\$\displaystyle \color{red}(x+y)(x-y)\color{black}-(x-y)^2\$

Hope this helps!!