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

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

Evaluate

$$8x^{2}-12y^{2}$$

Solution Steps

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

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

Combine -2xy and 2yx to get 0.

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

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

$$-x^{2}+4y^{2}-\left(-9x^{2}+12xy-12yx+16y^{2}\right)$$

Combine 12xy and -12yx to get 0.

$$-x^{2}+4y^{2}-\left(-9x^{2}+16y^{2}\right)$$

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

$$-x^{2}+4y^{2}-\left(-9x^{2}\right)-16y^{2}$$

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

$$-x^{2}+4y^{2}+9x^{2}-16y^{2}$$

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

$$8x^{2}+4y^{2}-16y^{2}$$

Combine 4y^{2} and -16y^{2} to get -12y^{2}.

$$8x^{2}-12y^{2}$$

Expand

$$8x^{2}-12y^{2}$$

Solution Steps

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

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

Combine -2xy and 2yx to get 0.

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

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

$$-x^{2}+4y^{2}-\left(-9x^{2}+12xy-12yx+16y^{2}\right)$$

Combine 12xy and -12yx to get 0.

$$-x^{2}+4y^{2}-\left(-9x^{2}+16y^{2}\right)$$

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

$$-x^{2}+4y^{2}-\left(-9x^{2}\right)-16y^{2}$$

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

$$-x^{2}+4y^{2}+9x^{2}-16y^{2}$$

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

$$8x^{2}+4y^{2}-16y^{2}$$

Combine 4y^{2} and -16y^{2} to get -12y^{2}.

$$8x^{2}-12y^{2}$$