Final answer:
The expression 48a + 40b is factored using the distributive law by first finding the GCF of 48 and 40, which is 8. The expression is then written in its factored form as 8(6a + 5b).
Step-by-step explanation:
To factor the expression 48a + 40b using the distributive law, we first need to find the greatest common factor (GCF) of the coefficients 48 and 40. The GCF of 48 and 40 is 8. To apply the distributive law, we factor out this GCF from each term in the expression.
We divide both terms by the GCF:
- 48a divided by 8 equals 6a.
- 40b divided by 8 equals 5b.
Now, we use the distributive law to write the expression as:
8(6a + 5b)
Therefore, the factored form of 48a + 40b using the distributive law is 8(6a + 5b).