Solve 8(4x^3-3x^2-1)-6(4x^3+8x-2)

$$8 ( 4 x ^ { 3 } - 3 x ^ { 2 } - 1 ) - 6 ( 4 x ^ { 3 } + 8 x - 2 )$$

Evaluate

$$8x^{3}-24x^{2}-48x+4$$

Solution Steps

Use the distributive property to multiply 8 by 4x^{3}-3x^{2}-1.

$$32x^{3}-24x^{2}-8-6\left(4x^{3}+8x-2\right)$$

Use the distributive property to multiply -6 by 4x^{3}+8x-2.

$$32x^{3}-24x^{2}-8-24x^{3}-48x+12$$

Combine 32x^{3} and -24x^{3} to get 8x^{3}.

$$8x^{3}-24x^{2}-8-48x+12$$

Add -8 and 12 to get 4.

$$8x^{3}-24x^{2}+4-48x$$

Expand

$$8x^{3}-24x^{2}-48x+4$$

Solution Steps

Use the distributive property to multiply 8 by 4x^{3}-3x^{2}-1.

$$32x^{3}-24x^{2}-8-6\left(4x^{3}+8x-2\right)$$

Use the distributive property to multiply -6 by 4x^{3}+8x-2.

$$32x^{3}-24x^{2}-8-24x^{3}-48x+12$$

Combine 32x^{3} and -24x^{3} to get 8x^{3}.

$$8x^{3}-24x^{2}-8-48x+12$$

Add -8 and 12 to get 4.

$$8x^{3}-24x^{2}+4-48x$$