distributive law to factor

Question

Use the distributive law to factor the following. Check multiplying.
40x + 8y + 24z = 2a+2b

Answer 1

On the left-hand side, the greatest common factor is 8, since 8 evenly divides 40, 8, and 24. The terms have no variables in common, so none can be factored out. Factor out an 8:

 

8(5x+y+3z)

 

Distribute the 8 on your own to make sure this is still equal to 40x+8y+24z.

 

 

On the right-hand side, the greatest common factor is 2, since 2 evenly divides 2 and 2. The terms have no variables in common, so none can be factored out. Factor out a 2:

 

2(a+b)

 

Distribute the 2 on your own to make sure this is still equal to 2a+2b.

 

 

Your factored equation is:

 

8(5x+y+3z) = 2(a+b)

 

 

You can divide both sides by 2 to get:

 

4(5x+y+3z) = a+b