Question

How can you use the distributive property to check your work when factoring?

Answer 1

A factor is any number that can be divided into another number evenly. When factoring, we look for common factors within a math expression. Factoring is normally used when finding common factors. The beauty of finding common factor is that it allows us to apply the distributive property usually applies multiplication to an existing mathematical expression such as an addition statement. This means that a number that is outside the parenthesis of an addition problem can be multiplied by each of the numbers inside the parenthesis. The opposite case is; a common factor can be factored out and written outside the parenthesis. 

Answer 2

The Distributive property applies multiplication to an existing addition statement. It means that a number outside the parentheses/brackets of an addition problem can be multiplied by each number inside the parentheses/brackets.

For example:

Let us consider factorization of

1. 10m + 25

It becomes 5(2m + 5)

2. 27m² + 18m

it becomes 9m(3m + 2)

So, in order to check if we are factorizing in the correct steps, we shall multiply the split factors and the answer should be the same as the factor that needed to be factorized. We will multiply (9m * 3m) +(9m *2) = 27m²+18m