Solve 64a^4-100b^2

$$64 a ^ { 4 } - 100 b ^ { 2 }$$

Factor

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

Solution Steps

Factor out 4.

$$4\left(16a^{4}-25b^{2}\right)$$

Consider 16a^{4}-25b^{2}. Rewrite 16a^{4}-25b^{2} as \left(4a^{2}\right)^{2}-\left(5b\right)^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

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

Rewrite the complete factored expression.

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

Evaluate

$$64a^{4}-100b^{2}$$