Solve 8x^4-200x^2y^4

$$8 x ^ { 4 } - 200 x ^ { 2 } y ^ { 4 }$$

Factor

$$8x^{2}\left(x-5y^{2}\right)\left(x+5y^{2}\right)$$

Solution Steps

Factor out 8.

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

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

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

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

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

Rewrite the complete factored expression.

$$8x^{2}\left(x-5y^{2}\right)\left(x+5y^{2}\right)$$

Evaluate

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