Solve (x+1)(x^2-24)(x+1)

$$(x+1)( { x }^{ 2 } -24)(x+1)$$

Evaluate

$$\left(x^{2}-24\right)\left(x+1\right)^{2}$$

Solution Steps

Multiply x+1 and x+1 to get \left(x+1\right)^{2}.

$$\left(x+1\right)^{2}\left(x^{2}-24\right)$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.

$$\left(x^{2}+2x+1\right)\left(x^{2}-24\right)$$

Use the distributive property to multiply x^{2}+2x+1 by x^{2}-24 and combine like terms.

$$x^{4}-23x^{2}+2x^{3}-48x-24$$

Expand

$$x^{4}+2x^{3}-23x^{2}-48x-24$$

Solution Steps

Multiply x+1 and x+1 to get \left(x+1\right)^{2}.

$$\left(x+1\right)^{2}\left(x^{2}-24\right)$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.

$$\left(x^{2}+2x+1\right)\left(x^{2}-24\right)$$

Use the distributive property to multiply x^{2}+2x+1 by x^{2}-24 and combine like terms.

$$x^{4}-23x^{2}+2x^{3}-48x-24$$