Solve 5(left(x-4right)^3-2(x-4))

$$5( { \left(x-4 \right) }^{ 3 } -2(x-4))$$

Evaluate

$$5\left(x-4\right)\left(\left(x-4\right)^{2}-2\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x-4\right)^{3}.

$$5\left(x^{3}-12x^{2}+48x-64-2\left(x-4\right)\right)$$

Use the distributive property to multiply -2 by x-4.

$$5\left(x^{3}-12x^{2}+48x-64-2x+8\right)$$

Combine 48x and -2x to get 46x.

$$5\left(x^{3}-12x^{2}+46x-64+8\right)$$

Add -64 and 8 to get -56.

$$5\left(x^{3}-12x^{2}+46x-56\right)$$

Use the distributive property to multiply 5 by x^{3}-12x^{2}+46x-56.

$$5x^{3}-60x^{2}+230x-280$$

Expand

$$5x^{3}-60x^{2}+230x-280$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x-4\right)^{3}.

$$5\left(x^{3}-12x^{2}+48x-64-2\left(x-4\right)\right)$$

Use the distributive property to multiply -2 by x-4.

$$5\left(x^{3}-12x^{2}+48x-64-2x+8\right)$$

Combine 48x and -2x to get 46x.

$$5\left(x^{3}-12x^{2}+46x-64+8\right)$$

Add -64 and 8 to get -56.

$$5\left(x^{3}-12x^{2}+46x-56\right)$$

Use the distributive property to multiply 5 by x^{3}-12x^{2}+46x-56.

$$5x^{3}-60x^{2}+230x-280$$