Solve x^2(x-1)(x+1)-x^2(x-2)(x+2)

$$x ^ { 2 } ( x - 1 ) ( x + 1 ) - x ^ { 2 } ( x - 2 ) ( x + 2 )$$

Evaluate

$$3x^{2}$$

Solution Steps

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

$$\left(x^{3}-x^{2}\right)\left(x+1\right)-x^{2}\left(x-2\right)\left(x+2\right)$$

Use the distributive property to multiply x^{3}-x^{2} by x+1 and combine like terms.

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

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

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

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

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

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

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

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

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

Combine -x^{2} and 4x^{2} to get 3x^{2}.

$$3x^{2}$$

Expand

$$3x^{2}$$

Solution Steps

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

$$\left(x^{3}-x^{2}\right)\left(x+1\right)-x^{2}\left(x-2\right)\left(x+2\right)$$

Use the distributive property to multiply x^{3}-x^{2} by x+1 and combine like terms.

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

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

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

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

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

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

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

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

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

Combine -x^{2} and 4x^{2} to get 3x^{2}.

$$3x^{2}$$