Solve 1/4(6u-5v)(36u^2+30uv+25v^2)

$$\frac { 1 } { 4 } ( 6 u - 5 v ) ( 36 u ^ { 2 } + 30 u v + 25 v ^ { 2 } )$$

Evaluate

$$-\frac{125v^{3}}{4}+54u^{3}$$

Solution Steps

Use the distributive property to multiply \frac{1}{4} by 6u-5v.

$$\left(\frac{3}{2}u-\frac{5}{4}v\right)\left(36u^{2}+30uv+25v^{2}\right)$$

Use the distributive property to multiply \frac{3}{2}u-\frac{5}{4}v by 36u^{2}+30uv+25v^{2} and combine like terms.

$$54u^{3}-\frac{125}{4}v^{3}$$

Expand

$$-\frac{125v^{3}}{4}+54u^{3}$$

Solution Steps

Use the distributive property to multiply \frac{1}{4} by 6u-5v.

$$\left(\frac{3}{2}u-\frac{5}{4}v\right)\left(36u^{2}+30uv+25v^{2}\right)$$

Use the distributive property to multiply \frac{3}{2}u-\frac{5}{4}v by 36u^{2}+30uv+25v^{2} and combine like terms.

$$54u^{3}-\frac{125}{4}v^{3}$$