Solve 2(x+y)^2-(x+2y)(x-5y)

$$2 ( x + y ) ^ { 2 } - ( x + 2 y ) ( x - 5 y )$$

Evaluate

$$\left(x+3y\right)\left(x+4y\right)$$

Solution Steps

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

$$2\left(x^{2}+2xy+y^{2}\right)-\left(x+2y\right)\left(x-5y\right)$$

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

$$2x^{2}+4xy+2y^{2}-\left(x+2y\right)\left(x-5y\right)$$

Use the distributive property to multiply x+2y by x-5y and combine like terms.

$$2x^{2}+4xy+2y^{2}-\left(x^{2}-3xy-10y^{2}\right)$$

To find the opposite of x^{2}-3xy-10y^{2}, find the opposite of each term.

$$2x^{2}+4xy+2y^{2}-x^{2}+3xy+10y^{2}$$

Combine 2x^{2} and -x^{2} to get x^{2}.

$$x^{2}+4xy+2y^{2}+3xy+10y^{2}$$

Combine 4xy and 3xy to get 7xy.

$$x^{2}+7xy+2y^{2}+10y^{2}$$

Combine 2y^{2} and 10y^{2} to get 12y^{2}.

$$x^{2}+7xy+12y^{2}$$

Expand

$$x^{2}+7xy+12y^{2}$$

Solution Steps

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

$$2\left(x^{2}+2xy+y^{2}\right)-\left(x+2y\right)\left(x-5y\right)$$

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

$$2x^{2}+4xy+2y^{2}-\left(x+2y\right)\left(x-5y\right)$$

Use the distributive property to multiply x+2y by x-5y and combine like terms.

$$2x^{2}+4xy+2y^{2}-\left(x^{2}-3xy-10y^{2}\right)$$

To find the opposite of x^{2}-3xy-10y^{2}, find the opposite of each term.

$$2x^{2}+4xy+2y^{2}-x^{2}+3xy+10y^{2}$$

Combine 2x^{2} and -x^{2} to get x^{2}.

$$x^{2}+4xy+2y^{2}+3xy+10y^{2}$$

Combine 4xy and 3xy to get 7xy.

$$x^{2}+7xy+2y^{2}+10y^{2}$$

Combine 2y^{2} and 10y^{2} to get 12y^{2}.

$$x^{2}+7xy+12y^{2}$$