Hi, can someone solve this for me? Thanks :)

Factorise fully:

(a^2-b^2)^2-(a-b)^4(a2b2)2(ab)4 =?

How do I work through this?

The solution is (4ab)(a-b)^2(4ab)(ab)2

1 Answer
Apr 28, 2018

"see explanation"see explanation

Explanation:

a^2-b^2" is a "color(blue)"difference of squares"a2b2 is a difference of squares

•color(white)(x)a^2-b^2=(a-b)(a+b)xa2b2=(ab)(a+b)

=((a-b)(a+b))^2-(a-b)^4=((ab)(a+b))2(ab)4

=(a-b)^2(a+b)^2-(a-b)^4=(ab)2(a+b)2(ab)4

"take out a "color(blue)"common factor "(a-b)^2take out a common factor (ab)2

=(a-b)^2((a+b)^2-(a-b)^2)=(ab)2((a+b)2(ab)2)

=(a-b)^2(a^2+2ab+b^2-(a^2-2ab+b^2))=(ab)2(a2+2ab+b2(a22ab+b2))

=(a-b)^2(cancel(a^2)+2abcancel(+b^2)cancel(-a^2)+2abcancel(-b^2))

=4ab(a-b)^2larr"as required"