Solve (3x-6)(4x^2-1)-(2x-4)(4x^2+4x+1)

$$(3x-6)(4 { x }^{ 2 } -1)-(2x-4)(4 { x }^{ 2 } +4x+1)$$

Evaluate

$$\left(x-2\right)\left(2x-5\right)\left(2x+1\right)$$

Solution Steps

Use the distributive property to multiply 3x-6 by 4x^{2}-1.

$$12x^{3}-3x-24x^{2}+6-\left(2x-4\right)\left(4x^{2}+4x+1\right)$$

Use the distributive property to multiply 2x-4 by 4x^{2}+4x+1 and combine like terms.

$$12x^{3}-3x-24x^{2}+6-\left(8x^{3}-8x^{2}-14x-4\right)$$

To find the opposite of 8x^{3}-8x^{2}-14x-4, find the opposite of each term.

$$12x^{3}-3x-24x^{2}+6-8x^{3}+8x^{2}+14x+4$$

Combine 12x^{3} and -8x^{3} to get 4x^{3}.

$$4x^{3}-3x-24x^{2}+6+8x^{2}+14x+4$$

Combine -24x^{2} and 8x^{2} to get -16x^{2}.

$$4x^{3}-3x-16x^{2}+6+14x+4$$

Combine -3x and 14x to get 11x.

$$4x^{3}+11x-16x^{2}+6+4$$

Add 6 and 4 to get 10.

$$4x^{3}+11x-16x^{2}+10$$

Expand

$$4x^{3}-16x^{2}+11x+10$$

Solution Steps

Use the distributive property to multiply 3x-6 by 4x^{2}-1.

$$12x^{3}-3x-24x^{2}+6-\left(2x-4\right)\left(4x^{2}+4x+1\right)$$

Use the distributive property to multiply 2x-4 by 4x^{2}+4x+1 and combine like terms.

$$12x^{3}-3x-24x^{2}+6-\left(8x^{3}-8x^{2}-14x-4\right)$$

To find the opposite of 8x^{3}-8x^{2}-14x-4, find the opposite of each term.

$$12x^{3}-3x-24x^{2}+6-8x^{3}+8x^{2}+14x+4$$

Combine 12x^{3} and -8x^{3} to get 4x^{3}.

$$4x^{3}-3x-24x^{2}+6+8x^{2}+14x+4$$

Combine -24x^{2} and 8x^{2} to get -16x^{2}.

$$4x^{3}-3x-16x^{2}+6+14x+4$$

Combine -3x and 14x to get 11x.

$$4x^{3}+11x-16x^{2}+6+4$$

Add 6 and 4 to get 10.

$$4x^{3}+11x-16x^{2}+10$$