Solve 3a^2x^3-12x^5

$$3 a ^ { 2 } x ^ { 3 } - 12 x ^ { 5 }$$

Factor

$$3\left(a-2x\right)\left(2x+a\right)x^{3}$$

Solution Steps

Factor out 3.

$$3\left(a^{2}x^{3}-4x^{5}\right)$$

Consider a^{2}x^{3}-4x^{5}. Factor out x^{3}.

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

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

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

Reorder the terms.

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

Rewrite the complete factored expression.

$$3x^{3}\left(-2x+a\right)\left(2x+a\right)$$

Evaluate

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