3m^3 + 27m = 3m(m^2 + 9)
= 3m(m + 3)(m – 3)
Right. What is your question?
To factor the expression 3m^3 + 27m, we can first look for a common factor between the two terms. In this case, the common factor is 3m.
Therefore, we can rewrite the expression as:
3m^3 + 27m = 3m(m^2 + 9)
Next, we can factor the expression inside the parentheses, m^2 + 9. This is a special case called the sum of squares, which cannot be factored further using real numbers. However, we can recognize that it follows the pattern of a^2 + b^2 = (a + b)(a - b), where a = m and b = 3i (since the square root of -9 is 3i).
So, we can rewrite the expression as:
3m^3 + 27m = 3m(m^2 + 9) = 3m(m + 3i)(m - 3i)
Therefore, the factored form is 3m(m + 3i)(m - 3i).