Solve -(2)(2x-3y)(3y+2x)-(4y-3x)(3x-4y)

$$- ( 2 ) ( 2 x - 3 y ) ( 3 y + 2 x ) - ( 4 y - 3 x ) ( 3 x - 4 y )$$

Evaluate

$$x^{2}-24xy+34y^{2}$$

Solution Steps

Use the distributive property to multiply -2 by 2x-3y.

$$\left(-4x+6y\right)\left(3y+2x\right)-\left(4y-3x\right)\left(3x-4y\right)$$

Apply the distributive property by multiplying each term of -4x+6y by each term of 3y+2x.

$$-12xy-8x^{2}+18y^{2}+12yx-\left(4y-3x\right)\left(3x-4y\right)$$

Combine -12xy and 12yx to get 0.

$$-8x^{2}+18y^{2}-\left(4y-3x\right)\left(3x-4y\right)$$

Apply the distributive property by multiplying each term of 4y-3x by each term of 3x-4y.

$$-8x^{2}+18y^{2}-\left(12yx-16y^{2}-9x^{2}+12yx\right)$$

Combine 12yx and 12yx to get 24yx.

$$-8x^{2}+18y^{2}-\left(24yx-16y^{2}-9x^{2}\right)$$

To find the opposite of 24yx-16y^{2}-9x^{2}, find the opposite of each term.

$$-8x^{2}+18y^{2}-24yx-\left(-16y^{2}\right)-\left(-9x^{2}\right)$$

The opposite of -16y^{2} is 16y^{2}.

$$-8x^{2}+18y^{2}-24yx+16y^{2}-\left(-9x^{2}\right)$$

The opposite of -9x^{2} is 9x^{2}.

$$-8x^{2}+18y^{2}-24yx+16y^{2}+9x^{2}$$

Combine 18y^{2} and 16y^{2} to get 34y^{2}.

$$-8x^{2}+34y^{2}-24yx+9x^{2}$$

Combine -8x^{2} and 9x^{2} to get x^{2}.

$$x^{2}+34y^{2}-24yx$$

Expand

$$x^{2}-24xy+34y^{2}$$

Solution Steps

Use the distributive property to multiply -2 by 2x-3y.

$$\left(-4x+6y\right)\left(3y+2x\right)-\left(4y-3x\right)\left(3x-4y\right)$$

Apply the distributive property by multiplying each term of -4x+6y by each term of 3y+2x.

$$-12xy-8x^{2}+18y^{2}+12yx-\left(4y-3x\right)\left(3x-4y\right)$$

Combine -12xy and 12yx to get 0.

$$-8x^{2}+18y^{2}-\left(4y-3x\right)\left(3x-4y\right)$$

Apply the distributive property by multiplying each term of 4y-3x by each term of 3x-4y.

$$-8x^{2}+18y^{2}-\left(12yx-16y^{2}-9x^{2}+12yx\right)$$

Combine 12yx and 12yx to get 24yx.

$$-8x^{2}+18y^{2}-\left(24yx-16y^{2}-9x^{2}\right)$$

To find the opposite of 24yx-16y^{2}-9x^{2}, find the opposite of each term.

$$-8x^{2}+18y^{2}-24yx-\left(-16y^{2}\right)-\left(-9x^{2}\right)$$

The opposite of -16y^{2} is 16y^{2}.

$$-8x^{2}+18y^{2}-24yx+16y^{2}-\left(-9x^{2}\right)$$

The opposite of -9x^{2} is 9x^{2}.

$$-8x^{2}+18y^{2}-24yx+16y^{2}+9x^{2}$$

Combine 18y^{2} and 16y^{2} to get 34y^{2}.

$$-8x^{2}+34y^{2}-24yx+9x^{2}$$

Combine -8x^{2} and 9x^{2} to get x^{2}.

$$x^{2}+34y^{2}-24yx$$