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

$$( x - 3 y ) ( 3 x + 2 y ) - 3 ( - 3 x - y ) ( x + 2 y )$$

Evaluate

$$2x\left(6x+7y\right)$$

Solution Steps

Apply the distributive property by multiplying each term of x-3y by each term of 3x+2y.

$$3x^{2}+2xy-9yx-6y^{2}-3\left(-3x-y\right)\left(x+2y\right)$$

Combine 2xy and -9yx to get -7xy.

$$3x^{2}-7xy-6y^{2}-3\left(-3x-y\right)\left(x+2y\right)$$

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

$$3x^{2}-7xy-6y^{2}+\left(9x+3y\right)\left(x+2y\right)$$

Apply the distributive property by multiplying each term of 9x+3y by each term of x+2y.

$$3x^{2}-7xy-6y^{2}+9x^{2}+18xy+3yx+6y^{2}$$

Combine 18xy and 3yx to get 21xy.

$$3x^{2}-7xy-6y^{2}+9x^{2}+21xy+6y^{2}$$

Combine 3x^{2} and 9x^{2} to get 12x^{2}.

$$12x^{2}-7xy-6y^{2}+21xy+6y^{2}$$

Combine -7xy and 21xy to get 14xy.

$$12x^{2}+14xy-6y^{2}+6y^{2}$$

Combine -6y^{2} and 6y^{2} to get 0.

$$12x^{2}+14xy$$

Expand

$$12x^{2}+14xy$$

Solution Steps

Apply the distributive property by multiplying each term of x-3y by each term of 3x+2y.

$$3x^{2}+2xy-9yx-6y^{2}-3\left(-3x-y\right)\left(x+2y\right)$$

Combine 2xy and -9yx to get -7xy.

$$3x^{2}-7xy-6y^{2}-3\left(-3x-y\right)\left(x+2y\right)$$

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

$$3x^{2}-7xy-6y^{2}+\left(9x+3y\right)\left(x+2y\right)$$

Apply the distributive property by multiplying each term of 9x+3y by each term of x+2y.

$$3x^{2}-7xy-6y^{2}+9x^{2}+18xy+3yx+6y^{2}$$

Combine 18xy and 3yx to get 21xy.

$$3x^{2}-7xy-6y^{2}+9x^{2}+21xy+6y^{2}$$

Combine 3x^{2} and 9x^{2} to get 12x^{2}.

$$12x^{2}-7xy-6y^{2}+21xy+6y^{2}$$

Combine -7xy and 21xy to get 14xy.

$$12x^{2}+14xy-6y^{2}+6y^{2}$$

Combine -6y^{2} and 6y^{2} to get 0.

$$12x^{2}+14xy$$