Question

factorization of 132?
a) $2^3 \cdot 3 \cdot 11$
b) $2^2 \cdot 3^2 \cdot 7$
c) $2^2 \cdot 3 \cdot 11$
d) $2^3 \cdot 3^2 \cdot 5$

which expression is equivalent to
$16 + 4 \cdot 36$
a) $2^3 + 2^2 \cdot 3$
b) $2^4 + 2^4 \cdot 3$
c) $2^3 + 2^3 \cdot 3^3$
d) $2^4 + 2^4 \cdot 3^2$

Explanation:

Step1: Prime factorize 132

$132 = 2 \times 2 \times 3 \times 11 = 2^2 \cdot 3 \cdot 11$

Step2: Verify the equivalent expression

First, rewrite $16 + 4 \cdot 36$ with primes:
$16 = 2^4$, $4=2^2$, $36=3^2$, so $4 \cdot 36 = 2^2 \cdot 3^2 = 2^4 \cdot 3^2$ (wait, correction: $4 \cdot 36 = 2^2 \cdot (2^2 \cdot 3^2) = 2^4 \cdot 3^2$; $16=2^4$. So $16 + 4 \cdot 36 = 2^4 + 2^4 \cdot 3^2$

Answer:

1. Factorization of 132: c) $2^2 \cdot 3 \cdot 11$
2. Equivalent expression for $16 + 4 \cdot 36$: d) $2^4 + 2^4 \cdot 3^2$