How do I factorise x(x + y)^2 - xy(x + y) and (x + y)^2 - 10(x + y)+25?

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I also need help to check if x^2(a - b) + y^2(b - a) = (a - b)(x + y)(x - y) and if ax - ay - bx + by = (x - y)(a - b)
Thanks!

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Answer 1 · 2018-05-11T08:57:56

Please see the explanation.

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

#(x + y)^2 - 10(x + y)+25#
Using: #a^2-2ab+b^2=(a-b)^2#:
#=[(x+y) - 5]^2=># Or:
#=(x+y-5)^2#

#x^2(a-b)+y^2(b-a)#
#=x^2(a-b)-y^2(a-b)#
#=(x^2-y^2)(a-b)#
#=(x-y)(x+y)(a-b)=># Correct

#ax-ay-bx+by#
#=a(x-y)-b(x-y)#
#=(x-y)(a-b)=>#Correct