Solve 8a^3x^4+64b^6x

$$8 a ^ { 3 } x ^ { 4 } + 64 b ^ { 6 } x$$

Factor

$$8x\left(ax+2b^{2}\right)\left(a^{2}x^{2}-2axb^{2}+4b^{4}\right)$$

Solution Steps

Factor out 8.

$$8\left(a^{3}x^{4}+8b^{6}x\right)$$

Consider a^{3}x^{4}+8b^{6}x. Factor out x.

$$x\left(a^{3}x^{3}+8b^{6}\right)$$

Consider a^{3}x^{3}+8b^{6}. Rewrite a^{3}x^{3}+8b^{6} as \left(ax\right)^{3}+\left(2b^{2}\right)^{3}. The sum of cubes can be factored using the rule: p^{3}+q^{3}=\left(p+q\right)\left(p^{2}-pq+q^{2}\right).

$$\left(ax+2b^{2}\right)\left(a^{2}x^{2}-2axb^{2}+4b^{4}\right)$$

Rewrite the complete factored expression.

$$8x\left(ax+2b^{2}\right)\left(a^{2}x^{2}-2axb^{2}+4b^{4}\right)$$

Evaluate

$$8x\left(\left(ax\right)^{3}+8b^{6}\right)$$