Find each product. See Examples 5 and 6. [(2p-3)+q]^2

Question

Accepted Answer

Welcome back. I am so glad you're here. We are given this expression bracket, parentheses seven a minus five and parentheses plus B. And bracket squared. And we are asked to perform the multiplication. So we're going to go through do the multiplication and then combine like terms to start. We are going to do the multiplication, indicated by this exponent here. By this squared. What that squared is saying is that we need to take what's in brackets and multiply it by itself. So we're taking parentheses seven a minus five plus B times seven A minus five plus B. And we are going to go through the foil process as you recall from previous lessons, that's multiplying the first and the first terms in this case are what's in parentheses here, the +78 minus five. And we're going to do the Outsides that's the +78 minus five times this Outside B. The Inside that's this B times the 78 minus five here. And the lasts which will be the B times the B. So let's go ahead and start doing that. So first I'm just going to write this out. First seven a minus five times seven a minus five. And then our Outsides they are positive. So it's plus seven a minus five times B. Our insides are the same thing plus B times seven a minus five. The order doesn't matter between those two and then our last our plus B times B. Now let's do the multiplication for the first one. We are going to foil again, we have two parentheses is being multiplied by each other. So our first again are +78 times seven A. That's going to be 49 A squared. Our Outsides 78 times negative five. That's minus 35 A. Insides negative five times seven A. That is minus 35 A. Again. And then lasts negative five times negative five is plus 25. Now for our um Outsides here in blue were going to take the B and distribute that to both of the terms inside the parentheses. So B times seven A. That's plus seven A. B. And B. Times negative five is minus five B. And for the green here the insides it's going to be the same thing. Be getting distributed to these two terms in the parentheses. So again 78 times B is plus seven A. B. And negative five times B. Is minus five B. And then the last year B times B is plus B squared. Now we just need to combine like terms I am going to put them in the order that we have for our answer choices. So that's a little bit easier to see. The first thing they have is the A. Squared. That's this first term. That's the only A squared. So that's 49 A. Squared. Next they have the B squared. So that's at the end here we've got plus B squared. Next they have the bees. So for RB terms we have a minus five B. And a minus five B. Negative five B. Plus negative five B. Is negative 10 B. The next terms they have are the A's. So that's negative 35 A minus 35 A. Which is minus 70 A. Next the Abbey's plus seven A. B. Plus seven A. B. That's plus 14 A. B. And the last constant term plus 25. Alright. We look at our answer choices and this matches with answer choice C. Well done, we'll catch you on the next one.

Find each product. See Examples 5 and 6. [(2p-3)+q]^2

Key Concepts

Binomial Expansion

Squaring a Binomial

Combining Like Terms

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