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

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

Evaluate

$$-4xy-y^{2}-9$$

Solution Steps

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

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

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

$$2\left(-y\right)x+\left(-y\right)y-4x^{2}-2xy-6x+4x^{2}-9+6x$$

Combine -6x and 6x to get 0.

$$2\left(-y\right)x+\left(-y\right)y-4x^{2}-2xy+4x^{2}-9$$

Combine -4x^{2} and 4x^{2} to get 0.

$$2\left(-y\right)x+\left(-y\right)y-2xy-9$$

Multiply 2 and -1 to get -2.

$$-2yx-yy-2xy-9$$

Multiply y and y to get y^{2}.

$$-2yx-y^{2}-2xy-9$$

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

$$-4yx-y^{2}-9$$

Expand

$$-4xy-y^{2}-9$$

Solution Steps

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

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

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

$$2\left(-y\right)x+\left(-y\right)y-4x^{2}-2xy-6x+4x^{2}-9+6x$$

Combine -6x and 6x to get 0.

$$2\left(-y\right)x+\left(-y\right)y-4x^{2}-2xy+4x^{2}-9$$

Combine -4x^{2} and 4x^{2} to get 0.

$$2\left(-y\right)x+\left(-y\right)y-2xy-9$$

Multiply 2 and -1 to get -2.

$$-2yx-yy-2xy-9$$

Multiply y and y to get y^{2}.

$$-2yx-y^{2}-2xy-9$$

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

$$-4yx-y^{2}-9$$