Solve 100x^6-16x^2y^8

$$100 x ^ { 6 } - 16 x ^ { 2 } y ^ { 8 }$$

Factor

$$4x^{2}\left(5x^{2}-2y^{4}\right)\left(5x^{2}+2y^{4}\right)$$

Solution Steps

Factor out 4.

$$4\left(25x^{6}-4x^{2}y^{8}\right)$$

Consider 25x^{6}-4x^{2}y^{8}. Factor out x^{2}.

$$x^{2}\left(25x^{4}-4y^{8}\right)$$

Consider 25x^{4}-4y^{8}. Rewrite 25x^{4}-4y^{8} as \left(5x^{2}\right)^{2}-\left(2y^{4}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(5x^{2}-2y^{4}\right)\left(5x^{2}+2y^{4}\right)$$

Rewrite the complete factored expression.

$$4x^{2}\left(5x^{2}-2y^{4}\right)\left(5x^{2}+2y^{4}\right)$$

Evaluate

$$100x^{6}-16x^{2}y^{8}$$