Simplify 3a^n(a^n+a^(n-1))

$3 a^{n} (a^{n} + a^{n - 1})$

Step 1

Apply the distributive property.

$3 a^{n} a^{n} + 3 a^{n} a^{n - 1}$

Step 2

Multiply $a^{n}$ by $a^{n}$ by adding the exponents.

Move $a^{n}$ .

$3 (a^{n} a^{n}) + 3 a^{n} a^{n - 1}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$3 a^{n + n} + 3 a^{n} a^{n - 1}$

Add $n$ and $n$ .

$3 a^{2 n} + 3 a^{n} a^{n - 1}$

Step 3

Multiply $a^{n}$ by $a^{n - 1}$ by adding the exponents.

Move $a^{n - 1}$ .

$3 a^{2 n} + 3 (a^{n - 1} a^{n})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$3 a^{2 n} + 3 a^{n - 1 + n}$

Add $n$ and $n$ .

$3 a^{2 n} + 3 a^{2 n - 1}$