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

$$f ( x ) = ( x - 1 ) ( x + 1 ) ^ { 2 } \times \frac { 1 } { 4 }$$

Evaluate

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

Solution Steps

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

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

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

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

Use the distributive property to multiply x^{3}+x^{2}-x-1 by \frac{1}{4}.

$$\frac{1}{4}x^{3}+\frac{1}{4}x^{2}-\frac{1}{4}x-\frac{1}{4}$$

Expand

$$\frac{x^{3}+x^{2}-x-1}{4}$$

Solution Steps

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

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

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

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

Use the distributive property to multiply x^{3}+x^{2}-x-1 by \frac{1}{4}.

$$\frac{1}{4}x^{3}+\frac{1}{4}x^{2}-\frac{1}{4}x-\frac{1}{4}$$