Solve x^2(x^2-4)+4x(x^2-4)+4(x^2-4)

$$x ^ { 2 } ( x ^ { 2 } - 4 ) + 4 x ( x ^ { 2 } - 4 ) + 4 ( x ^ { 2 } - 4 )$$

Evaluate

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

Solution Steps

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

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

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

$$x^{4}-4x^{2}+4x^{3}-16x+4\left(x^{2}-4\right)$$

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

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

Combine -4x^{2} and 4x^{2} to get 0.

$$x^{4}+4x^{3}-16x-16$$

Expand

$$x^{4}+4x^{3}-16x-16$$

Solution Steps

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

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

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

$$x^{4}-4x^{2}+4x^{3}-16x+4\left(x^{2}-4\right)$$

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

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

Combine -4x^{2} and 4x^{2} to get 0.

$$x^{4}+4x^{3}-16x-16$$