How do you factor #2x^2 (x + y) - y(x + y)^2#?

1 Answer
Jim G.
May 16, 2018

#(x+y)(x-y)(2x+y)#

Explanation:

#"take out a "color(blue)"common factor "(x+y)#

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

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

#"factorise "2x^2-xy-y^2" using the a-c method"#

#"the factors of the product "2xx-1=-2#

#"which sum to - 1 are - 2 and + 1"#

#"split the middle term using these factors"#

#2x^2-2xy+xy-y^2larrcolor(blue)"factor by grouping"#

#=color(red)(2x)(x-y)color(red)(+y)(x-y)#

#"take out the "color(blue)"common factor "(x-y)#

#=(x-y)(color(red)(2x+y))#

#rArr2x^2(x+y)-y(x+y)^2=(x+y(x-y)(2x+y)#

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