How do you factor #2x^2 (x + y) - y(x + y)^2#?
1 Answer
May 16, 2018
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)#
