In this video, we will look at simplifying a variable expression using the Distributive Property. Let's recall what the Distributive Property says. It says that if a, b, and c are real numbers, then a times the quantity of (b + c) is equal to ab + ac or the quantity of (b + c)a is equal to ba + ca. So for example, if we have 3 times a quantity of (5 + 2), is that equal to (3 times 5 plus 3 times 2)? The Distributive Property says that the left side will be equal to the right side. On the left side, we would do the addition inside the parentheses first. Five plus 2 is 7. So we would have 3 times 7. On the right side, we would do the multiplication first. Three times 5 is 15. To that we're adding 3 times 2, which is 6. On the left side, 3 times 7 is 21. And on the right side, 15 plus 6 is 21. We can use the Distributive Property to remove parentheses in a variable expression. Let's look at some examples of how that works. Simplify. Here we have the variable expression 5 times the quantity of (3 + 7b), so to simplify this variable expression, we're going to use the Distributive Property to remove the parentheses. So using that Distributive Property, we're going to multiply 5 by each of the terms inside the parentheses. So we'll start by multiplying 5 by 3, and so we have 5 times 3. Into that, we had the product of 5 and the second term inside the parentheses, 7b. So plus 5 times 7b. So we have 5 times 3. That's 15. To simplify 5 times 7b, let's use the Associative Property of Multiplication to group the 5 and 7 together. And that product will be the coefficient on b. Five times 7 is 35. So our simplified form is 15 + 35b. Let's try another example. Simplify. Here we have the quantity of (3a - 1)5. So we have a quantity in parentheses being multiplied by a number on the right, but we can still use the Distributive Property. And to do that, we're going to multiply each term inside the parentheses by 5. So we'll start by multiplying 3a by 5 and so we will have 3a times 5. From that we're going to subtract the product of 1 and 5. So we multiply 1, the second term inside the parentheses, by 5. So simplifying here, we can use the Associative and Commutative of Properties of Multiplication to rewrite this as 3 times 5 times a. And from that, we're subtracting 1 times 5, which is 5. Three times 5 is 15. So 15 is the coefficient on a, and the first term. And our simplified form is 15a - 5.