Solve 7ab^2-28a^3

$$7 a b ^ { 2 } - 28 a ^ { 3 }$$

Factor

$$7a\left(b-2a\right)\left(2a+b\right)$$

Solution Steps

Factor out 7.

$$7\left(ab^{2}-4a^{3}\right)$$

Consider ab^{2}-4a^{3}. Factor out a.

$$a\left(b^{2}-4a^{2}\right)$$

Consider b^{2}-4a^{2}. Rewrite b^{2}-4a^{2} as b^{2}-\left(2a\right)^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

$$\left(b-2a\right)\left(b+2a\right)$$

Reorder the terms.

$$\left(-2a+b\right)\left(2a+b\right)$$

Rewrite the complete factored expression.

$$7a\left(-2a+b\right)\left(2a+b\right)$$

Evaluate

$$7a\left(b^{2}-4a^{2}\right)$$