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

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

Evaluate

$$24x^{2}-17xy-44y^{2}$$

Solution Steps

Apply the distributive property by multiplying each term of 4x-y by each term of 7x+4y.

$$28x^{2}+16xy-7yx-4y^{2}-\left(2x+8y\right)\left(2x+5y\right)$$

Combine 16xy and -7yx to get 9xy.

$$28x^{2}+9xy-4y^{2}-\left(2x+8y\right)\left(2x+5y\right)$$

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

$$28x^{2}+9xy-4y^{2}-\left(4x^{2}+10xy+16xy+40y^{2}\right)$$

Combine 10xy and 16xy to get 26xy.

$$28x^{2}+9xy-4y^{2}-\left(4x^{2}+26xy+40y^{2}\right)$$

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

$$28x^{2}+9xy-4y^{2}-4x^{2}-26xy-40y^{2}$$

Combine 28x^{2} and -4x^{2} to get 24x^{2}.

$$24x^{2}+9xy-4y^{2}-26xy-40y^{2}$$

Combine 9xy and -26xy to get -17xy.

$$24x^{2}-17xy-4y^{2}-40y^{2}$$

Combine -4y^{2} and -40y^{2} to get -44y^{2}.

$$24x^{2}-17xy-44y^{2}$$

Expand

$$24x^{2}-17xy-44y^{2}$$

Solution Steps

Apply the distributive property by multiplying each term of 4x-y by each term of 7x+4y.

$$28x^{2}+16xy-7yx-4y^{2}-\left(2x+8y\right)\left(2x+5y\right)$$

Combine 16xy and -7yx to get 9xy.

$$28x^{2}+9xy-4y^{2}-\left(2x+8y\right)\left(2x+5y\right)$$

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

$$28x^{2}+9xy-4y^{2}-\left(4x^{2}+10xy+16xy+40y^{2}\right)$$

Combine 10xy and 16xy to get 26xy.

$$28x^{2}+9xy-4y^{2}-\left(4x^{2}+26xy+40y^{2}\right)$$

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

$$28x^{2}+9xy-4y^{2}-4x^{2}-26xy-40y^{2}$$

Combine 28x^{2} and -4x^{2} to get 24x^{2}.

$$24x^{2}+9xy-4y^{2}-26xy-40y^{2}$$

Combine 9xy and -26xy to get -17xy.

$$24x^{2}-17xy-4y^{2}-40y^{2}$$

Combine -4y^{2} and -40y^{2} to get -44y^{2}.

$$24x^{2}-17xy-44y^{2}$$