Question

Which expression shows a way to factor 36 + 27?
3(12 + 8)
3(11 + 8)
9(4 + 2)
9(4 + 3)

Answer 1

To factor the expression \(36 + 27\), we first calculate the sum:

\[
36 + 27 = 63
\]

Next, we find the factors of \(63\). The prime factorization of \(63\) is:

\[
63 = 3^2 \cdot 7
\]

From here, we see that \(63\) can be factored into:

1. \(3(21)\)
2. \(7(9)\)
3. \(9(7)\)

Now, let’s look at the options given:

1. \(3(12 + 8) = 3(20) = 60\) (not correct)
2. \(3(11 + 8) = 3(19) = 57\) (not correct)
3. \(9(4 + 2) = 9(6) = 54\) (not correct)
4. \(9(4 + 3) = 9(7) = 63\) (correct)

The correct expression that shows a way to factor \(36 + 27\) is:

\[
\boxed{9(4 + 3)}
\]