Solve 3v^2w-21vw-3v^2+21v

$$3 v ^ { 2 } w - 21 v w - 3 v ^ { 2 } + 21 v$$

Factor

$$3v\left(v-7\right)\left(w-1\right)$$

Solution Steps

Factor out 3.

$$3\left(v^{2}w-7vw-v^{2}+7v\right)$$

Consider v^{2}w-7vw-v^{2}+7v. Factor out v.

$$v\left(vw-7w-v+7\right)$$

Consider vw-7w-v+7. Do the grouping vw-7w-v+7=\left(vw-7w\right)+\left(-v+7\right), and factor out w in the first and -1 in the second group.

$$w\left(v-7\right)-\left(v-7\right)$$

Factor out common term v-7 by using distributive property.

$$\left(v-7\right)\left(w-1\right)$$

Rewrite the complete factored expression.

$$3v\left(v-7\right)\left(w-1\right)$$

Evaluate

$$3v\left(v-7\right)\left(w-1\right)$$