Solve (2x-5y-4)(8x-2y+1)-(2-4x)(-2-4x)-10(-4x)

$$( 2 x - 5 y - 4 ) ( 8 x - 2 y + 1 ) - ( 2 - 4 x ) ( - 2 - 4 x ) - 10 ( - 4 x )$$

Evaluate

$$3y+10y^{2}+10x-44xy$$

Solution Steps

Apply the distributive property by multiplying each term of 2x-5y-4 by each term of 8x-2y+1.

$$16x^{2}-4xy+2x-40yx+10y^{2}-5y-32x+8y-4-\left(2-4x\right)\left(-2-4x\right)-10\left(-4\right)x$$

Combine -4xy and -40yx to get -44xy.

$$16x^{2}-44xy+2x+10y^{2}-5y-32x+8y-4-\left(2-4x\right)\left(-2-4x\right)-10\left(-4\right)x$$

Combine 2x and -32x to get -30x.

$$16x^{2}-44xy-30x+10y^{2}-5y+8y-4-\left(2-4x\right)\left(-2-4x\right)-10\left(-4\right)x$$

Combine -5y and 8y to get 3y.

$$16x^{2}-44xy-30x+10y^{2}+3y-4-\left(2-4x\right)\left(-2-4x\right)-10\left(-4\right)x$$

Apply the distributive property by multiplying each term of 2-4x by each term of -2-4x.

$$16x^{2}-44xy-30x+10y^{2}+3y-4-\left(-4-8x+8x+16x^{2}\right)-10\left(-4\right)x$$

Combine -8x and 8x to get 0.

$$16x^{2}-44xy-30x+10y^{2}+3y-4-\left(-4+16x^{2}\right)-10\left(-4\right)x$$

To find the opposite of -4+16x^{2}, find the opposite of each term.

$$16x^{2}-44xy-30x+10y^{2}+3y-4-\left(-4\right)-16x^{2}-10\left(-4\right)x$$

The opposite of -4 is 4.

$$16x^{2}-44xy-30x+10y^{2}+3y-4+4-16x^{2}-10\left(-4\right)x$$

Add -4 and 4 to get 0.

$$16x^{2}-44xy-30x+10y^{2}+3y-16x^{2}-10\left(-4\right)x$$

Combine 16x^{2} and -16x^{2} to get 0.

$$-44xy-30x+10y^{2}+3y-10\left(-4\right)x$$

Multiply 10 and -4 to get -40.

$$-44xy-30x+10y^{2}+3y-\left(-40x\right)$$

The opposite of -40x is 40x.

$$-44xy-30x+10y^{2}+3y+40x$$

Combine -30x and 40x to get 10x.

$$-44xy+10x+10y^{2}+3y$$

Expand

$$3y+10y^{2}+10x-44xy$$

Solution Steps

Apply the distributive property by multiplying each term of 2x-5y-4 by each term of 8x-2y+1.

$$16x^{2}-4xy+2x-40yx+10y^{2}-5y-32x+8y-4-\left(2-4x\right)\left(-2-4x\right)-10\left(-4\right)x$$

Combine -4xy and -40yx to get -44xy.

$$16x^{2}-44xy+2x+10y^{2}-5y-32x+8y-4-\left(2-4x\right)\left(-2-4x\right)-10\left(-4\right)x$$

Combine 2x and -32x to get -30x.

$$16x^{2}-44xy-30x+10y^{2}-5y+8y-4-\left(2-4x\right)\left(-2-4x\right)-10\left(-4\right)x$$

Combine -5y and 8y to get 3y.

$$16x^{2}-44xy-30x+10y^{2}+3y-4-\left(2-4x\right)\left(-2-4x\right)-10\left(-4\right)x$$

Apply the distributive property by multiplying each term of 2-4x by each term of -2-4x.

$$16x^{2}-44xy-30x+10y^{2}+3y-4-\left(-4-8x+8x+16x^{2}\right)-10\left(-4\right)x$$

Combine -8x and 8x to get 0.

$$16x^{2}-44xy-30x+10y^{2}+3y-4-\left(-4+16x^{2}\right)-10\left(-4\right)x$$

To find the opposite of -4+16x^{2}, find the opposite of each term.

$$16x^{2}-44xy-30x+10y^{2}+3y-4-\left(-4\right)-16x^{2}-10\left(-4\right)x$$

The opposite of -4 is 4.

$$16x^{2}-44xy-30x+10y^{2}+3y-4+4-16x^{2}-10\left(-4\right)x$$

Add -4 and 4 to get 0.

$$16x^{2}-44xy-30x+10y^{2}+3y-16x^{2}-10\left(-4\right)x$$

Combine 16x^{2} and -16x^{2} to get 0.

$$-44xy-30x+10y^{2}+3y-10\left(-4\right)x$$

Multiply 10 and -4 to get -40.

$$-44xy-30x+10y^{2}+3y-\left(-40x\right)$$

The opposite of -40x is 40x.

$$-44xy-30x+10y^{2}+3y+40x$$

Combine -30x and 40x to get 10x.

$$-44xy+10x+10y^{2}+3y$$