Solve (x-1/2)(x^2+1/4)(x+1/2)

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

Evaluate

$$x^{4}-\frac{1}{16}$$

Solution Steps

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

$$\left(x^{3}+\frac{1}{4}x-\frac{1}{2}x^{2}-\frac{1}{8}\right)\left(x+\frac{1}{2}\right)$$

Use the distributive property to multiply x^{3}+\frac{1}{4}x-\frac{1}{2}x^{2}-\frac{1}{8} by x+\frac{1}{2} and combine like terms.

$$x^{4}-\frac{1}{16}$$

Expand

$$x^{4}-\frac{1}{16}$$

Solution Steps

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

$$\left(x^{3}+\frac{1}{4}x-\frac{1}{2}x^{2}-\frac{1}{8}\right)\left(x+\frac{1}{2}\right)$$

Use the distributive property to multiply x^{3}+\frac{1}{4}x-\frac{1}{2}x^{2}-\frac{1}{8} by x+\frac{1}{2} and combine like terms.

$$x^{4}-\frac{1}{16}$$