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)

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