Solve 7(x+y)^2+13y(x+y)-2y^2

$$7 ( x + y ) ^ { 2 } + 13 y ( x + y ) - 2 y ^ { 2 }$$

Evaluate

$$\left(x+3y\right)\left(7x+6y\right)$$

Solution Steps

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

$$7\left(x^{2}+2xy+y^{2}\right)+13y\left(x+y\right)-2y^{2}$$

Use the distributive property to multiply 7 by x^{2}+2xy+y^{2}.

$$7x^{2}+14xy+7y^{2}+13y\left(x+y\right)-2y^{2}$$

Use the distributive property to multiply 13y by x+y.

$$7x^{2}+14xy+7y^{2}+13yx+13y^{2}-2y^{2}$$

Combine 14xy and 13yx to get 27xy.

$$7x^{2}+27xy+7y^{2}+13y^{2}-2y^{2}$$

Combine 7y^{2} and 13y^{2} to get 20y^{2}.

$$7x^{2}+27xy+20y^{2}-2y^{2}$$

Combine 20y^{2} and -2y^{2} to get 18y^{2}.

$$7x^{2}+27xy+18y^{2}$$

Expand

$$7x^{2}+27xy+18y^{2}$$

Solution Steps

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

$$7\left(x^{2}+2xy+y^{2}\right)+13y\left(x+y\right)-2y^{2}$$

Use the distributive property to multiply 7 by x^{2}+2xy+y^{2}.

$$7x^{2}+14xy+7y^{2}+13y\left(x+y\right)-2y^{2}$$

Use the distributive property to multiply 13y by x+y.

$$7x^{2}+14xy+7y^{2}+13yx+13y^{2}-2y^{2}$$

Combine 14xy and 13yx to get 27xy.

$$7x^{2}+27xy+7y^{2}+13y^{2}-2y^{2}$$

Combine 7y^{2} and 13y^{2} to get 20y^{2}.

$$7x^{2}+27xy+20y^{2}-2y^{2}$$

Combine 20y^{2} and -2y^{2} to get 18y^{2}.

$$7x^{2}+27xy+18y^{2}$$