Use the distributive law to factor the following: Check by multiplying.
22x+11y+55z =
22x+11y+55z
There is a common factor of 11
=11(2x+y+5z)
Multiply and you will get back to 22x+11y+55z
Use the distributive law to factor 66u+66v
To factor the expression 22x + 11y + 55z using the distributive law, we need to find the greatest common factor of all terms.
Step 1: Identify the greatest common factor (GCF) of all terms.
In this case, the GCF is 11, since it is a common factor of 22, 11, and 55.
Step 2: Divide each term by the GCF.
To factor out the GCF, divide each term by 11:
22x ÷ 11 = 2x
11y ÷ 11 = y
55z ÷ 11 = 5z
Step 3: Write the factored expression.
The factored expression is:
11(2x + y + 5z)
To check if we factored correctly, we can multiply the factored expression to see if we obtain the original expression:
11(2x + y + 5z) =
11 * 2x + 11 * y + 11 * 5z =
22x + 11y + 55z
Since the multiplication yields the original expression, we can conclude that we factored correctly.