1. The problem is to simplify the expression $x^2 + x^2$. 2. The formula used here is the addition of like terms: $a^n + a^n = 2a^n$. 3. Since both terms are $x^2$, they are like terms and can be added by adding their coefficients. 4. Each $x^2$ has an implicit coefficient of 1, so $1x^2 + 1x^2 = (1+1)x^2 = 2x^2$. 5. Therefore, the simplified expression is $2x^2$.