Factor a^(5n)+a^(2n)

usually we factor out the power with the smaller exponent, so

a^(5n) + a^(2n)
= a^(2n) (a^(3n) + 1)

Thank You :)

To factor the expression a^(5n) + a^(2n), we can first observe that both terms have a common factor of a^(2n). We can then rewrite the expression as:

a^(2n) * (a^(3n) + 1)

Now, let's focus on factoring the expression within the parentheses (a^(3n) + 1). This can be done by recognizing it as a sum of cubes. Recall the sum of cubes formula:

a^3 + b^3 = (a + b)(a^2 - ab + b^2)

We can apply this formula by considering a^(3n) as a cube and 1 as the second term:

a^(3n) + 1 = (a^n)^3 + 1^3

Using the sum of cubes formula, we can factor it as:

(a^n + 1)(a^(2n) - a^n + 1)

Therefore, the factored form of the expression a^(5n) + a^(2n) is:

a^(2n) * (a^n + 1)(a^(2n) - a^n + 1)