An Intro to the Distributive Property Simplifying Expressions Math with Mr J

Welcome to Math with Mr. In this video, I'm going to go through an introduction to simplifying algebraic expressions using the distributive property. Now, the distributive property can help us remove parentheses within algebraic expressions. This helps us simplify expressions when we do not have like terms within parentheses that we can combine. Now, remember, when we have something next to parentheses, that means multiplication. So, we can use the distributive property to distribute whatever is on the outside of the parentheses to the terms inside the parentheses. The distributive property works when we have addition or subtraction inside of the parentheses. So, at the top of the screen, there is general overview of the distributive property where is being distributed to the terms inside of the parentheses. The distributive property and that overview will make lot more sense as we go through our examples. Let's jump into number one where we have two and then in parentheses 5 + 3. And we're going to do this two different ways by using the order of operations, so doing what's in the parentheses first, and then also using the distributive property. Now, for number one, we don't have any variables involved. We are actually able to add what's in the parentheses first and then go from there. We don't have to use the distributive property, but the point of number one is to show us that we get the same thing either way. This is going to show us that the distributive property doesn't change the value of an expression. We are able to use this strategy. So, again, we get the same thing either way. Let's start by using the order of operations and doing what's in the parentheses first. We have 5 + 3, which is 8. Bring down the two. And now we have 2 * 8, which is 16. Now, let's use the distributive property and see if we still get 16. So, we need to take that two on the outside of the parentheses and distribute it to the five and to the three. So, we have two * 5 + two * 3. 2 * 5 gives us 10. + 2 * 3 gives us 6. 10 + 6 is 16. So, we get 16 that way, as well. So, we can see that the distributive property doesn't change the value of an expression, and we are able to use it. Let's move on to number two, where we will apply this to an algebraic expression in order to simplify the expression. We are going to remove the parentheses. For number two, we have 8 and then in parentheses 2m + 6. Now, we can't combine those terms in the parentheses. So, what we can do, we can use the distributive property to remove those parentheses and simplify this expression. So, let's distribute the 8 to the 2m and to the 6. This gives us 8 * 2m + * 6. 8 * 2m is 16m + 8 * 6 is 48. Now, 16m and 48 are unlike terms. So, we don't have any terms that we can combine. So, we are done here. 16m + 48 is our simplified expression. Let's move on to number three, where we have seven and then in parentheses minus nine. Let's distribute that seven to the and to the nine. That gives us seven * minus, bring the subtraction sign down, seven * 9. 7 * is just 7a minus 7 * 9 is 63. So, we end up with 7a - 63. We don't have any like terms that we can combine. So, we are simplified and done. Again, 7a - 63. Now, do want to mention another way to think through this, and this is another way to think through whenever subtraction or negatives are involved. So, let me rewrite the expression and then distribute the seven. So, we have 7 * which is 7a, and then we can think of that subtraction sign and the nine as negative nine. So, including the sign in front with the nine. So, we think of that as negative nine. So, let's distribute that seven to the negative nine. 7 * -9 is negative 63. So, negative 63. And we get 7a 63 that way, as well. And again, that's just different way to think through it. You get the same thing either way, but you can include the sign in front of the term and think of that as negative nine. So, something to keep in mind. Let's move on to number four, where we have 10 and then in parentheses -5x 4y. Let's distribute the 10 to the -5x and to the 4y. So, 10 * -5x * 4 10 * -5x gives us negative 50x 10 * 4y gives us 40 So, we end up with -50x - 40y. We don't have any like terms that we can combine. So, we are done. Again, -50x - 40y. Now, let's take look at different way to think through this. So, will rewrite the expression off to the side. So, let's distribute the 10 to the negative 5x, and then we will think of that as negative 4y. So, include the sign in front of that term. 10 * -5x is negative 50x, and then 10 * -4y is negative 40y. So, we get the same thing that way, as well. -50x 40y. So, there you have it. There's an introduction to the distributive property. Check the description for link to part two, where go through four more examples. hope that helped. Thanks so much for watching. Until next time. Peace.