Solve a^2c+5a^2d-b^2c-5b^2d

$$a ^ { 2 } c + 5 a ^ { 2 } d - b ^ { 2 } c - 5 b ^ { 2 } d$$

Factor

$$\left(a-b\right)\left(a+b\right)\left(c+5d\right)$$

Solution Steps

Do the grouping a^{2}c+5a^{2}d-b^{2}c-5b^{2}d=\left(a^{2}c+5a^{2}d\right)+\left(-b^{2}c-5b^{2}d\right), and factor out a^{2} in the first and -b^{2} in the second group.

$$a^{2}\left(c+5d\right)-b^{2}\left(c+5d\right)$$

Factor out common term c+5d by using distributive property.

$$\left(c+5d\right)\left(a^{2}-b^{2}\right)$$

Consider a^{2}-b^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

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

Rewrite the complete factored expression.

$$\left(a-b\right)\left(a+b\right)\left(c+5d\right)$$

Evaluate

$$\left(c+5d\right)\left(a^{2}-b^{2}\right)$$