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

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

Evaluate

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

Solution Steps

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

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

Multiply 2 and -2 to get -4.

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

The opposite of -4\left(3x^{2}-4+2x\right)x^{3} is 4\left(3x^{2}-4+2x\right)x^{3}.

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

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

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

Use the distributive property to multiply 12x^{2}-16+8x by x^{3}.

$$-6x^{5}+38x^{3}+4x^{4}-12x^{2}-56x-16+12x^{5}-16x^{3}+8x^{4}$$

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

$$6x^{5}+38x^{3}+4x^{4}-12x^{2}-56x-16-16x^{3}+8x^{4}$$

Combine 38x^{3} and -16x^{3} to get 22x^{3}.

$$6x^{5}+22x^{3}+4x^{4}-12x^{2}-56x-16+8x^{4}$$

Combine 4x^{4} and 8x^{4} to get 12x^{4}.

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

Expand

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

Solution Steps

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

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

Multiply 2 and -2 to get -4.

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

The opposite of -4\left(3x^{2}-4+2x\right)x^{3} is 4\left(3x^{2}-4+2x\right)x^{3}.

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

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

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

Use the distributive property to multiply 12x^{2}-16+8x by x^{3}.

$$-6x^{5}+38x^{3}+4x^{4}-12x^{2}-56x-16+12x^{5}-16x^{3}+8x^{4}$$

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

$$6x^{5}+38x^{3}+4x^{4}-12x^{2}-56x-16-16x^{3}+8x^{4}$$

Combine 38x^{3} and -16x^{3} to get 22x^{3}.

$$6x^{5}+22x^{3}+4x^{4}-12x^{2}-56x-16+8x^{4}$$

Combine 4x^{4} and 8x^{4} to get 12x^{4}.

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