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

$$( 3 ) ( 3 x - y ) ( 3 x + y ) + y ( x + y )$$

Evaluate

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

Solution Steps

Use the distributive property to multiply 3 by 3x-y.

$$\left(9x-3y\right)\left(3x+y\right)+y\left(x+y\right)$$

Apply the distributive property by multiplying each term of 9x-3y by each term of 3x+y.

$$27x^{2}+9xy-9yx-3y^{2}+y\left(x+y\right)$$

Combine 9xy and -9yx to get 0.

$$27x^{2}-3y^{2}+y\left(x+y\right)$$

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

$$27x^{2}-3y^{2}+yx+y^{2}$$

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

$$27x^{2}-2y^{2}+yx$$

Expand

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

Solution Steps

Use the distributive property to multiply 3 by 3x-y.

$$\left(9x-3y\right)\left(3x+y\right)+y\left(x+y\right)$$

Apply the distributive property by multiplying each term of 9x-3y by each term of 3x+y.

$$27x^{2}+9xy-9yx-3y^{2}+y\left(x+y\right)$$

Combine 9xy and -9yx to get 0.

$$27x^{2}-3y^{2}+y\left(x+y\right)$$

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

$$27x^{2}-3y^{2}+yx+y^{2}$$

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

$$27x^{2}-2y^{2}+yx$$