Solve (x+1)*(x^2-1)*(4+x^3)=

$$( x + 1 ) \cdot ( x ^ { 2 } - 1 ) \cdot ( 4 + x ^ { 3 } ) =$$

Evaluate

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

Solution Steps

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

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

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

$$3x^{3}+x^{6}-4x-x^{4}+4x^{2}+x^{5}-4$$

Expand

$$x^{6}+x^{5}-x^{4}+3x^{3}+4x^{2}-4x-4$$

Solution Steps

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

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

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

$$3x^{3}+x^{6}-4x-x^{4}+4x^{2}+x^{5}-4$$