Solve (-8x+14)*(x^2-2x+2)-2*(2x-2)*(-4x^2+14x-6)=

$$(-8x+14) \times ( { x }^{ 2 } -2x+2)-2 \times (2x-2) \times (-4 { x }^{ 2 } +14x-6)=$$

Evaluate

$$8x^{3}-42x^{2}+36x+4$$

Solution Steps

Use the distributive property to multiply -8x+14 by x^{2}-2x+2 and combine like terms.

$$-8x^{3}+30x^{2}-44x+28-2\left(2x-2\right)\left(-4x^{2}+14x-6\right)$$

Use the distributive property to multiply -2 by 2x-2.

$$-8x^{3}+30x^{2}-44x+28+\left(-4x+4\right)\left(-4x^{2}+14x-6\right)$$

Use the distributive property to multiply -4x+4 by -4x^{2}+14x-6 and combine like terms.

$$-8x^{3}+30x^{2}-44x+28+16x^{3}-72x^{2}+80x-24$$

Combine -8x^{3} and 16x^{3} to get 8x^{3}.

$$8x^{3}+30x^{2}-44x+28-72x^{2}+80x-24$$

Combine 30x^{2} and -72x^{2} to get -42x^{2}.

$$8x^{3}-42x^{2}-44x+28+80x-24$$

Combine -44x and 80x to get 36x.

$$8x^{3}-42x^{2}+36x+28-24$$

Subtract 24 from 28 to get 4.

$$8x^{3}-42x^{2}+36x+4$$

Expand

$$8x^{3}-42x^{2}+36x+4$$

Solution Steps

Use the distributive property to multiply -8x+14 by x^{2}-2x+2 and combine like terms.

$$-8x^{3}+30x^{2}-44x+28-2\left(2x-2\right)\left(-4x^{2}+14x-6\right)$$

Use the distributive property to multiply -2 by 2x-2.

$$-8x^{3}+30x^{2}-44x+28+\left(-4x+4\right)\left(-4x^{2}+14x-6\right)$$

Use the distributive property to multiply -4x+4 by -4x^{2}+14x-6 and combine like terms.

$$-8x^{3}+30x^{2}-44x+28+16x^{3}-72x^{2}+80x-24$$

Combine -8x^{3} and 16x^{3} to get 8x^{3}.

$$8x^{3}+30x^{2}-44x+28-72x^{2}+80x-24$$

Combine 30x^{2} and -72x^{2} to get -42x^{2}.

$$8x^{3}-42x^{2}-44x+28+80x-24$$

Combine -44x and 80x to get 36x.

$$8x^{3}-42x^{2}+36x+28-24$$

Subtract 24 from 28 to get 4.

$$8x^{3}-42x^{2}+36x+4$$