Solve 5^4-a^4

$$5 ^ { 4 } - a ^ { 4 }$$

Factor

$$\left(a-5\right)\left(a+5\right)\left(-a^{2}-25\right)$$

Solution Steps

Rewrite 625-a^{4} as 25^{2}-\left(a^{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).

$$\left(25-a^{2}\right)\left(25+a^{2}\right)$$

Reorder the terms.

$$\left(-a^{2}+25\right)\left(a^{2}+25\right)$$

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

$$\left(5-a\right)\left(5+a\right)$$

Reorder the terms.

$$\left(-a+5\right)\left(a+5\right)$$

Rewrite the complete factored expression. Polynomial a^{2}+25 is not factored since it does not have any rational roots.

$$\left(-a+5\right)\left(a+5\right)\left(a^{2}+25\right)$$

Evaluate

$$625-a^{4}$$

Solution Steps

Calculate 5 to the power of 4 and get 625.

$$625-a^{4}$$