Solve f(x)=(x+1)^3e^-1

$$f ( x ) = ( x + 1 ) ^ { 3 } e ^ { - 1 }$$

Evaluate

$$\frac{\left(x+1\right)^{3}}{e}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(x+1\right)^{3}.

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

Use the distributive property to multiply x^{3}+3x^{2}+3x+1 by e^{-1}.

$$x^{3}e^{-1}+3x^{2}e^{-1}+3xe^{-1}+e^{-1}$$

Expand

$$\frac{x^{3}+3x^{2}+3x+1}{e}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(x+1\right)^{3}.

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

Use the distributive property to multiply x^{3}+3x^{2}+3x+1 by e^{-1}.

$$x^{3}e^{-1}+3x^{2}e^{-1}+3xe^{-1}+e^{-1}$$