Solve x(x+1)(x+1)1/6

$$x(x+1)(x+1) \frac{ 1 }{ 6 }$$

Evaluate

$$\frac{x\left(x+1\right)^{2}}{6}$$

Solution Steps

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

$$x\left(x+1\right)^{2}\times \frac{1}{6}$$

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

$$x\left(x^{2}+2x+1\right)\times \frac{1}{6}$$

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

$$\left(x^{3}+2x^{2}+x\right)\times \frac{1}{6}$$

Use the distributive property to multiply x^{3}+2x^{2}+x by \frac{1}{6}.

$$x^{3}\times \frac{1}{6}+2x^{2}\times \frac{1}{6}+x\times \frac{1}{6}$$

Multiply 2 and \frac{1}{6} to get \frac{2}{6}.

$$x^{3}\times \frac{1}{6}+\frac{2}{6}x^{2}+x\times \frac{1}{6}$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$x^{3}\times \frac{1}{6}+\frac{1}{3}x^{2}+x\times \frac{1}{6}$$

Expand

$$\frac{x^{3}}{6}+\frac{x^{2}}{3}+\frac{x}{6}$$

Solution Steps

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

$$x\left(x+1\right)^{2}\times \frac{1}{6}$$

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

$$x\left(x^{2}+2x+1\right)\times \frac{1}{6}$$

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

$$\left(x^{3}+2x^{2}+x\right)\times \frac{1}{6}$$

Use the distributive property to multiply x^{3}+2x^{2}+x by \frac{1}{6}.

$$x^{3}\times \frac{1}{6}+2x^{2}\times \frac{1}{6}+x\times \frac{1}{6}$$

Multiply 2 and \frac{1}{6} to get \frac{2}{6}.

$$x^{3}\times \frac{1}{6}+\frac{2}{6}x^{2}+x\times \frac{1}{6}$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$x^{3}\times \frac{1}{6}+\frac{1}{3}x^{2}+x\times \frac{1}{6}$$