Solve 3v^4x^3-48x^3

$$3 v ^ { 4 } x ^ { 3 } - 48 x ^ { 3 }$$

Factor

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

Solution Steps

Factor out 3.

$$3\left(v^{4}x^{3}-16x^{3}\right)$$

Consider v^{4}x^{3}-16x^{3}. Factor out x^{3}.

$$x^{3}\left(v^{4}-16\right)$$

Consider v^{4}-16. Rewrite v^{4}-16 as \left(v^{2}\right)^{2}-4^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(v^{2}-4\right)\left(v^{2}+4\right)$$

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

$$\left(v-2\right)\left(v+2\right)$$

Rewrite the complete factored expression. Polynomial v^{2}+4 is not factored since it does not have any rational roots.

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

Evaluate

$$3x^{3}\left(v^{4}-16\right)$$