Solve (x+1/2)(x+5)(4x^2-1)

$$( x + \frac { 1 } { 2 } ) ( x + 5 ) ( 4 x ^ { 2 } - 1 )$$

Evaluate

$$\frac{\left(2x-1\right)\left(x+5\right)\left(2x+1\right)^{2}}{2}$$

Solution Steps

Use the distributive property to multiply x+\frac{1}{2} by x+5 and combine like terms.

$$\left(x^{2}+\frac{11}{2}x+\frac{5}{2}\right)\left(4x^{2}-1\right)$$

Use the distributive property to multiply x^{2}+\frac{11}{2}x+\frac{5}{2} by 4x^{2}-1 and combine like terms.

$$4x^{4}+9x^{2}+22x^{3}-\frac{11}{2}x-\frac{5}{2}$$

Expand

$$4x^{4}+22x^{3}+9x^{2}-\frac{11x}{2}-\frac{5}{2}$$

Solution Steps

Use the distributive property to multiply x+\frac{1}{2} by x+5 and combine like terms.

$$\left(x^{2}+\frac{11}{2}x+\frac{5}{2}\right)\left(4x^{2}-1\right)$$

Use the distributive property to multiply x^{2}+\frac{11}{2}x+\frac{5}{2} by 4x^{2}-1 and combine like terms.

$$4x^{4}+9x^{2}+22x^{3}-\frac{11}{2}x-\frac{5}{2}$$