Solve 625x^4-16b^4

$$625 x ^ { 4 } - 16 b ^ { 4 }$$

Factor

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

Solution Steps

Rewrite 625x^{4}-16b^{4} as \left(25x^{2}\right)^{2}-\left(4b^{2}\right)^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

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

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

$$\left(5x-2b\right)\left(5x+2b\right)$$

Rewrite the complete factored expression.

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

Evaluate

$$625x^{4}-16b^{4}$$