Factor the Expression: Breaking Down 3x³+6a⁴ Step by Step

Factor the following expression:

$3x^3+6a^4$

Note that in the given expression there are two completely different terms, meaning - the letters cannot be factored out. Hence we will factor out the greatest common factor of the numbers 6 and 3, which is clearly the number 3 and is a factor of both other numbers:$3x^3+6a^4 =3(x^3+2a^4)$

After factoring out the common factor outside the parentheses, we will look at each term before factoring out the common factor. We must ask ourselves "By how much did we multiply the common factor to get the current term?" Continue to fill in the missing parts inside the parentheses whilst making sure that the sign of the term we completed inside the parentheses when multiplied by the sign of the term we factored out will give us the sign of the original term. It is recommended to verify that the factoring was done correctly by opening the parentheses, performing the multiplications and confirming that we indeed obtain the expression before factoring.

Therefore, the correct answer is answer B.