Question

3. 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

Answer 2

$\rm{\left(x+y\right)\left(2x+y\right)+\left(x+2y\right)\left(x-y\right)}$

$\rm{=2x^2+3xy+y^2+\left(x+2y\right)\left(x-y\right)}$

$\rm{=2x^2+3xy+y^2+x^2+xy-2y^2}$

$\rm{=2x^2+x^2+3xy+xy+y^2-2y^2}$

$\rm{=3x^2+3xy+xy+y^2-2y^2}$

$\rm{=3x^2+4xy+y^2-2y^2}$

$\rm{=3x^2+4xy-y^2}$