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

$$4x-44y^{2}-33xy-4x^{2}$$

Solution Steps

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

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

To find the opposite of 7yx+4y^{2}, find the opposite of each term.

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

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

$$4x-7yx-4y^{2}-\left(4x^{2}+10xy+16yx+40y^{2}\right)$$

Combine 10xy and 16yx to get 26xy.

$$4x-7yx-4y^{2}-\left(4x^{2}+26xy+40y^{2}\right)$$

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

$$4x-7yx-4y^{2}-4x^{2}-26xy-40y^{2}$$

Combine -7yx and -26xy to get -33yx.

$$4x-33yx-4y^{2}-4x^{2}-40y^{2}$$

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

$$4x-33yx-44y^{2}-4x^{2}$$

Expand

$$4x-44y^{2}-33xy-4x^{2}$$

Solution Steps

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

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

To find the opposite of 7yx+4y^{2}, find the opposite of each term.

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

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

$$4x-7yx-4y^{2}-\left(4x^{2}+10xy+16yx+40y^{2}\right)$$

Combine 10xy and 16yx to get 26xy.

$$4x-7yx-4y^{2}-\left(4x^{2}+26xy+40y^{2}\right)$$

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

$$4x-7yx-4y^{2}-4x^{2}-26xy-40y^{2}$$

Combine -7yx and -26xy to get -33yx.

$$4x-33yx-4y^{2}-4x^{2}-40y^{2}$$

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

$$4x-33yx-44y^{2}-4x^{2}$$