Solve 2(x+y)^2+(3x-y)^2

$$2 ( x + y ) ^ { 2 } + ( 3 x - y ) ^ { 2 }$$

Expand

$$11x^{2}-2xy+3y^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+y\right)^{2}.

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

Use the distributive property to multiply 2 by x^{2}+2xy+y^{2}.

$$2x^{2}+4xy+2y^{2}+\left(3x-y\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-y\right)^{2}.

$$2x^{2}+4xy+2y^{2}+9x^{2}-6xy+y^{2}$$

Combine 2x^{2} and 9x^{2} to get 11x^{2}.

$$11x^{2}+4xy+2y^{2}-6xy+y^{2}$$

Combine 4xy and -6xy to get -2xy.

$$11x^{2}-2xy+2y^{2}+y^{2}$$

Combine 2y^{2} and y^{2} to get 3y^{2}.

$$11x^{2}-2xy+3y^{2}$$

Evaluate

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

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+y\right)^{2}.

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

Use the distributive property to multiply 2 by x^{2}+2xy+y^{2}.

$$2x^{2}+4xy+2y^{2}+\left(3x-y\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-y\right)^{2}.

$$2x^{2}+4xy+2y^{2}+9x^{2}-6xy+y^{2}$$

Combine 2x^{2} and 9x^{2} to get 11x^{2}.

$$11x^{2}+4xy+2y^{2}-6xy+y^{2}$$

Combine 4xy and -6xy to get -2xy.

$$11x^{2}-2xy+2y^{2}+y^{2}$$

Combine 2y^{2} and y^{2} to get 3y^{2}.

$$11x^{2}-2xy+3y^{2}$$