Question

simplify


(x+y) (2x+y) +(x+2y) (x-y)​

Answer 1

(x+y)(2x+y)+(x+2y)(x−y)

=x(2x+y)+y(2x+y)+x(x−y)+2y(x−y)

=2x 2 +xy+2xy+y

2 +x 2 −xy+2xy−2y 2

=(2+1)x 2 +(1+2−1+2)xy+(1−2)y 2

=3x 2 +4xy−y 2

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Answer 2

x+y)(2x+y)+(x+2y)(x−y)

=x(2x+y)+y(2x+y)+x(x−y)+2y(x−y)

=2x 2 +xy+2xy+y

2 +x 2 −xy+2xy−2y 2

=(2+1)x 2 +(1+2−1+2)xy+(1−2)y 2

=3x 2 +4xy−y 2