Question

Explain how to use the Distributive Property in reverse to write an equivalent expression for 40x + 56. Then tell how to check the expressions to verify that they are equivalent.

Answer 1

To factor an expression like 40x + 56 using the Distributive Property in reverse, we find the greatest common factor, which is 8, and then express the original sum as: 8(5x + 7). To verify that the expressions are equivalent, we redistribute the 8 to get the original expression back.

Step-by-step explanation:

To use the Distributive Property in reverse to write an equivalent expression for 40x + 56, we look for a common factor that we can factor out of both terms. The greatest common factor (GCF) for 40 and 56 is 8. So, we can write:

40x + 56 = 8(5x + 7)

This process is sometimes referred to as 'factoring out' the GCF. The Distributive Property dictates that a(b + c) = ab + ac, and this process can also work in reverse, allowing us to take ab + ac and factor it into a(b + c).

To verify that the expressions are equivalent, we can distribute the 8 back into each term within the parentheses:

8(5x) + 8(7) = 40x + 56

Next, multiply each term:

40x + 56 = 40x + 56

Now we see that the original expression and the factored expression are indeed equivalent.