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

Factorise fully:

#(a^2-b^2)^2-(a-b)^4# =?

How do I work through this?

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

1 Answer
Jim G.
Apr 28, 2018

#"see explanation"#

Explanation:

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

#•color(white)(x)a^2-b^2=(a-b)(a+b)#

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

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

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

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

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

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

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

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