Final answer:
The expression 6y + 6z + 27 is factored by first finding the GCF, which is 3, and then factoring further to get 3(2(y + z) + 9), written as a product with a whole number greater than 1.
Step-by-step explanation:
To factor the expression 6y + 6z + 27, we need to find the greatest common factor (GCF) of the terms.
We notice that each term is divisible by 3.
Dividing each term by 3, we get 2y + 2z + 9. So we factor out the 3 and rewrite the expression as 3(2y + 2z + 9).
However, we can factor further by noticing that 2y and 2z also have a common factor of 2.
By factoring 2 out of 2y + 2z, we get 2(y + z).
We substitute this back into the expression to get 3(2(y + z) + 9).
After factoring, our final expression is 3(2(y + z) + 9) which is written as a product with a whole number greater than 1.
Always check your answer to ensure it is reasonable by distributing the 3 back into the parentheses and confirming you get the original expression.