Factor \( 12 a+7 a^{3} \)

To factor the expression \( 12a + 7a^3 \), you start by identifying the common factor in both terms. Here, the common factor is \( a \). Factoring out \( a \) gives us: \[ a(12 + 7a^2) \] Now the expression is factored completely as \( a(12 + 7a^2) \). Moving on to a neat little trick: Always look for common factors first, just like finding the last piece of a puzzle! If you spot any variable or numerical commonality, you're already halfway there to a more elegant expression.