Solve 4u(3v+2u)-v^2(v-7)

$$4 u ( 3 v + 2 u ) - v ^ { 2 } ( v - 7 )$$

Evaluate

$$-\left(v-7\right)v^{2}+4u\left(2u+3v\right)$$

Solution Steps

Use the distributive property to multiply 4u by 3v+2u.

$$12uv+8u^{2}-v^{2}\left(v-7\right)$$

Use the distributive property to multiply v^{2} by v-7.

$$12uv+8u^{2}-\left(v^{3}-7v^{2}\right)$$

To find the opposite of v^{3}-7v^{2}, find the opposite of each term.

$$12uv+8u^{2}-v^{3}+7v^{2}$$

Expand

$$8u^{2}+12uv-v^{3}+7v^{2}$$

Solution Steps

Use the distributive property to multiply 4u by 3v+2u.

$$12uv+8u^{2}-v^{2}\left(v-7\right)$$

Use the distributive property to multiply v^{2} by v-7.

$$12uv+8u^{2}-\left(v^{3}-7v^{2}\right)$$

To find the opposite of v^{3}-7v^{2}, find the opposite of each term.

$$12uv+8u^{2}-v^{3}+7v^{2}$$