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

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

Expand

$$x^{5}+x^{4}-3x^{3}-3x^{2}-4x-4$$

Solution Steps

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

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

Use the distributive property to multiply x^{3}-4x+x^{2}-4 by x^{2}+1 and combine like terms.

$$x^{5}-3x^{3}-4x+x^{4}-3x^{2}-4$$

Evaluate

$$\left(x+1\right)\left(x^{2}-4\right)\left(x^{2}+1\right)$$

Solution Steps

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

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

Use the distributive property to multiply x^{3}-4x+x^{2}-4 by x^{2}+1 and combine like terms.

$$x^{5}-3x^{3}-4x+x^{4}-3x^{2}-4$$