Solve (-6x^2+10x+4)*(x^3-4x+x^2-4)-2*(3x^2-4+2x)*(-2{x}^3+5{x}^2+4x-12)=

$$(-6 { x }^{ 2 } +10x+4) \times ( { x }^{ 3 } -4x+ { x }^{ 2 } -4)-2 \times (3 { x }^{ 2 } -4+2x) \times (-2 { x }^{ 3 } +5 { x }^{ 2 } +4x-12)=$$

Evaluate

$$-2\left(3x^{2}+9x+7\right)\left(2-x\right)^{3}$$

Solution Steps

Use the distributive property to multiply -6x^{2}+10x+4 by x^{3}-4x+x^{2}-4 and combine like terms.

$$-6x^{5}+38x^{3}+4x^{4}-12x^{2}-56x-16-2\left(3x^{2}-4+2x\right)\left(-2x^{3}+5x^{2}+4x-12\right)$$

Use the distributive property to multiply -2 by 3x^{2}-4+2x.

$$-6x^{5}+38x^{3}+4x^{4}-12x^{2}-56x-16+\left(-6x^{2}+8-4x\right)\left(-2x^{3}+5x^{2}+4x-12\right)$$

Use the distributive property to multiply -6x^{2}+8-4x by -2x^{3}+5x^{2}+4x-12 and combine like terms.

$$-6x^{5}+38x^{3}+4x^{4}-12x^{2}-56x-16+12x^{5}-22x^{4}-60x^{3}+96x^{2}+80x-96$$

Combine -6x^{5} and 12x^{5} to get 6x^{5}.

$$6x^{5}+38x^{3}+4x^{4}-12x^{2}-56x-16-22x^{4}-60x^{3}+96x^{2}+80x-96$$

Combine 4x^{4} and -22x^{4} to get -18x^{4}.

$$6x^{5}+38x^{3}-18x^{4}-12x^{2}-56x-16-60x^{3}+96x^{2}+80x-96$$

Combine 38x^{3} and -60x^{3} to get -22x^{3}.

$$6x^{5}-22x^{3}-18x^{4}-12x^{2}-56x-16+96x^{2}+80x-96$$

Combine -12x^{2} and 96x^{2} to get 84x^{2}.

$$6x^{5}-22x^{3}-18x^{4}+84x^{2}-56x-16+80x-96$$

Combine -56x and 80x to get 24x.

$$6x^{5}-22x^{3}-18x^{4}+84x^{2}+24x-16-96$$

Subtract 96 from -16 to get -112.

$$6x^{5}-22x^{3}-18x^{4}+84x^{2}+24x-112$$

Expand

$$6x^{5}-18x^{4}-22x^{3}+84x^{2}+24x-112$$

Solution Steps

Use the distributive property to multiply -6x^{2}+10x+4 by x^{3}-4x+x^{2}-4 and combine like terms.

$$-6x^{5}+38x^{3}+4x^{4}-12x^{2}-56x-16-2\left(3x^{2}-4+2x\right)\left(-2x^{3}+5x^{2}+4x-12\right)$$

Use the distributive property to multiply -2 by 3x^{2}-4+2x.

$$-6x^{5}+38x^{3}+4x^{4}-12x^{2}-56x-16+\left(-6x^{2}+8-4x\right)\left(-2x^{3}+5x^{2}+4x-12\right)$$

Use the distributive property to multiply -6x^{2}+8-4x by -2x^{3}+5x^{2}+4x-12 and combine like terms.

$$-6x^{5}+38x^{3}+4x^{4}-12x^{2}-56x-16+12x^{5}-22x^{4}-60x^{3}+96x^{2}+80x-96$$

Combine -6x^{5} and 12x^{5} to get 6x^{5}.

$$6x^{5}+38x^{3}+4x^{4}-12x^{2}-56x-16-22x^{4}-60x^{3}+96x^{2}+80x-96$$

Combine 4x^{4} and -22x^{4} to get -18x^{4}.

$$6x^{5}+38x^{3}-18x^{4}-12x^{2}-56x-16-60x^{3}+96x^{2}+80x-96$$

Combine 38x^{3} and -60x^{3} to get -22x^{3}.

$$6x^{5}-22x^{3}-18x^{4}-12x^{2}-56x-16+96x^{2}+80x-96$$

Combine -12x^{2} and 96x^{2} to get 84x^{2}.

$$6x^{5}-22x^{3}-18x^{4}+84x^{2}-56x-16+80x-96$$

Combine -56x and 80x to get 24x.

$$6x^{5}-22x^{3}-18x^{4}+84x^{2}+24x-16-96$$

Subtract 96 from -16 to get -112.

$$6x^{5}-22x^{3}-18x^{4}+84x^{2}+24x-112$$