Solve 16x^8-625y^4

$$16 x ^ { 8 } - 625 y ^ { 4 }$$

Factor

$$\left(2x^{2}-5y\right)\left(2x^{2}+5y\right)\left(4x^{4}+25y^{2}\right)$$

Solution Steps

Rewrite 16x^{8}-625y^{4} as \left(4x^{4}\right)^{2}-\left(25y^{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).

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

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

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

Rewrite the complete factored expression.

$$\left(2x^{2}-5y\right)\left(2x^{2}+5y\right)\left(4x^{4}+25y^{2}\right)$$

Evaluate

$$16x^{8}-625y^{4}$$