Solve (4x-x)(7y+4x)-(2y+8x)(2y+5x)

$$(4x-x)(7y+4x)-(2y+8x)(2y+5x)$$

Evaluate

$$-28x^{2}-5xy-4y^{2}$$

Solution Steps

Combine 4x and -x to get 3x.

$$3x\left(7y+4x\right)-\left(2y+8x\right)\left(2y+5x\right)$$

Use the distributive property to multiply 3x by 7y+4x.

$$21xy+12x^{2}-\left(2y+8x\right)\left(2y+5x\right)$$

Apply the distributive property by multiplying each term of 2y+8x by each term of 2y+5x.

$$21xy+12x^{2}-\left(4y^{2}+10yx+16xy+40x^{2}\right)$$

Combine 10yx and 16xy to get 26yx.

$$21xy+12x^{2}-\left(4y^{2}+26yx+40x^{2}\right)$$

To find the opposite of 4y^{2}+26yx+40x^{2}, find the opposite of each term.

$$21xy+12x^{2}-4y^{2}-26yx-40x^{2}$$

Combine 21xy and -26yx to get -5xy.

$$-5xy+12x^{2}-4y^{2}-40x^{2}$$

Combine 12x^{2} and -40x^{2} to get -28x^{2}.

$$-5xy-28x^{2}-4y^{2}$$

Expand

$$-28x^{2}-5xy-4y^{2}$$

Solution Steps

Combine 4x and -x to get 3x.

$$3x\left(7y+4x\right)-\left(2y+8x\right)\left(2y+5x\right)$$

Use the distributive property to multiply 3x by 7y+4x.

$$21xy+12x^{2}-\left(2y+8x\right)\left(2y+5x\right)$$

Apply the distributive property by multiplying each term of 2y+8x by each term of 2y+5x.

$$21xy+12x^{2}-\left(4y^{2}+10yx+16xy+40x^{2}\right)$$

Combine 10yx and 16xy to get 26yx.

$$21xy+12x^{2}-\left(4y^{2}+26yx+40x^{2}\right)$$

To find the opposite of 4y^{2}+26yx+40x^{2}, find the opposite of each term.

$$21xy+12x^{2}-4y^{2}-26yx-40x^{2}$$

Combine 21xy and -26yx to get -5xy.

$$-5xy+12x^{2}-4y^{2}-40x^{2}$$

Combine 12x^{2} and -40x^{2} to get -28x^{2}.

$$-5xy-28x^{2}-4y^{2}$$