Solve 13a^{3}b-13a^3c+13a^3b^2-13a^3bc

$$13 a ^ { 3 } b - 13 a ^ { 3 } c + 13 a ^ { 3 } b ^ { 2 } - 13 a ^ { 3 } b c$$

Factor

$$13\left(b+1\right)\left(b-c\right)a^{3}$$

Solution Steps

Factor out 13.

$$13\left(a^{3}b-a^{3}c+a^{3}b^{2}-a^{3}bc\right)$$

Consider a^{3}b-a^{3}c+a^{3}b^{2}-a^{3}bc. Factor out a^{3}.

$$a^{3}\left(b-c+b^{2}-bc\right)$$

Consider b-c+b^{2}-bc. Do the grouping b-c+b^{2}-bc=\left(b-c\right)+\left(b^{2}-bc\right), and factor out b in b^{2}-bc.

$$b-c+b\left(b-c\right)$$

Factor out common term b-c by using distributive property.

$$\left(b-c\right)\left(1+b\right)$$

Rewrite the complete factored expression.

$$13a^{3}\left(b+1\right)\left(b-c\right)$$

Evaluate

$$13\left(b+1\right)\left(b-c\right)a^{3}$$