use the distributive law to factor the following and check 3+27b+6c

Remember when using the distributive law to factor you are in fact using factoring backwards.

Write each of your terms with the common multiplyer. Do you see the connection between all the numbers?
What number in the equation is the base for the rest. 3,right?

So write each term with 3 as you would as 27 and 6 as the answer.

Then you have 3(9b+2c)+3

When you check multiply each term in the parentheses and add three.
3x9b=27b
3x2c=6c
+3
Does that make sense?

To factor the expression 3+27b+6c using the distributive law, we need to find the Greatest Common Factor (GCF) of the three terms and then rewrite the expression in the form of the GCF multiplied by the factored expression.

Step 1: Find the GCF
In this case, the GCF of 3, 27b, and 6c is 3, as each term is divisible by 3.

Step 2: Divide each term by the GCF
Dividing each term by 3, we get:
(3/3) + (27b/3) + (6c/3)
which simplifies to:
1 + 9b + 2c

So, the factored form of 3+27b+6c using the distributive law is 1 + 9b + 2c.

To check the factoring, you can distribute the GCF back in and see if the original expression is obtained. Let's verify:

Distributing the GCF of 3:
3(1) + 3(9b) + 3(2c)
which simplifies to:
3 + 27b + 6c

Thus, the original expression 3+27b+6c is correctly factored as 1 + 9b + 2c.