Solve 256x^4-625y^4

$$256 x ^ { 4 } - 625 y ^ { 4 }$$

Factor

$$\left(4x-5y\right)\left(4x+5y\right)\left(16x^{2}+25y^{2}\right)$$

Solution Steps

Rewrite 256x^{4}-625y^{4} as \left(16x^{2}\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).

$$\left(16x^{2}-25y^{2}\right)\left(16x^{2}+25y^{2}\right)$$

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

$$\left(4x-5y\right)\left(4x+5y\right)$$

Rewrite the complete factored expression.

$$\left(4x-5y\right)\left(4x+5y\right)\left(16x^{2}+25y^{2}\right)$$

Evaluate

$$256x^{4}-625y^{4}$$