The expression 27 + 45 as a product using the GCF and distributive property.

(a) By Greatest Common Factor: (27 + 45) = 3 (9 + 15)

(b) By distributive property: (27 + 45) = 9 (3) + 9 (5)

Step-by-step explanation:

Here, the given expression is 27 + 45.

Now, by Prime Factorization:

27 = 3 x 3 x 3

45 = 3 x 3 x 5

Here, the 3 is the ONLY prime common factor.

So, the Greatest Common Factor = 3

⇒ (27 + 45) = 3 (9 + 15)

Hence, by Greatest Common Factor: (27 + 45) = 3 (9 + 15)

Now, by distributive property:

A (B + C) = AB + AC

Here, in the given expression:

(27 + 45) = 9 (3 + 5) = 9 (3) + 9 (5)

or, (27 + 45) = 9 (3) + 9 (5)

Hence, by distributive property: (27 + 45) = 9 (3) + 9 (5)