Solve -(1/4p-1)(3p^2+p-8)

$$- ( \frac { 1 } { 4 } p - 1 ) ( 3 p ^ { 2 } + p - 8 )$$

Evaluate

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

Solution Steps

To find the opposite of \frac{1}{4}p-1, find the opposite of each term.

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

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

$$-\frac{3}{4}p^{3}+\frac{11}{4}p^{2}+3p-8$$

Expand

$$-\frac{3p^{3}}{4}+\frac{11p^{2}}{4}+3p-8$$

Solution Steps

To find the opposite of \frac{1}{4}p-1, find the opposite of each term.

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

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

$$-\frac{3}{4}p^{3}+\frac{11}{4}p^{2}+3p-8$$