Question

Use the distributive property to rewrite the expression as a multiple of a sum of two numbers with no common factor.

A) 6 + 27
B) 6×(2+9)
C) 3×(20+27)
D) 3×(2+9)
E) 6×(62+9)

Answer 1

To rewrite the expression 3×(20+27) using the distributive property and ensuring no common factors within the sum, we factor out the greatest common factor, resulting in 3×3×(6+9).

Step-by-step explanation:

To use the distributive property to rewrite the expression as a multiple of a sum of two numbers with no common factor, let's look at choice C) 3×(20+27). Here, we can consider the greatest common factor (GCF) of the numbers within the parentheses, which is 3. To apply the distributive property and to assure that the sum inside the parentheses has no common factors, we divide both numbers by the common factor 3 and factor it out.

So, the operation would look like the following:
C) 3×(20+27) can be rewritten as 3×(3×6+3×9) = 3×3×(6+9).

Now, the expression is factored completely, and (6+9) has no common factors other than 1.