Solve (8)(x-1/2)(x^2+1/4)(x+1/2)

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

Evaluate

$$8x^{4}-\frac{1}{2}$$

Solution Steps

Use the distributive property to multiply 8 by x-\frac{1}{2}.

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

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

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

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

$$8x^{4}-\frac{1}{2}$$

Expand

$$8x^{4}-\frac{1}{2}$$

Solution Steps

Use the distributive property to multiply 8 by x-\frac{1}{2}.

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

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

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

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

$$8x^{4}-\frac{1}{2}$$