SAT Math Part 6 - Factoring Perfect Square Trinomials - By The Organic Chemistry Tutor
Transcript
| 00:00 | number 23 . If two X plus three Y . | |
| 00:04 | Is equal to four , what is the value of | |
| 00:09 | four X squared plus 12 X . Y plus nine | |
| 00:11 | Y squared . So what do you think we need | |
| 00:14 | to do in this problem ? So notice that four | |
| 00:20 | X squared is the square of two X . And | |
| 00:24 | nine Y squared is the square of three Y . | |
| 00:27 | So this indicates that we potentially have a perfect square | |
| 00:31 | . Try no meal . Now to be certain multiply | |
| 00:35 | two X by three Y . That's going to give | |
| 00:37 | you six X . Y . And then double it | |
| 00:39 | when you double it , you get 12 X . | |
| 00:40 | Y . If that third condition is met then you | |
| 00:44 | do indeed have a perfect square train Romeo . So | |
| 00:49 | let's start with what we're given two acts plus three | |
| 00:52 | . Y . Is equal to four . Now what | |
| 00:55 | we're gonna do is we're gonna take the square of | |
| 00:58 | both sides . So let's foil two X . Plus | |
| 01:06 | three Y . Times another copy and four square to | |
| 01:09 | 16 . So two X times two X . We | |
| 01:13 | know it's gonna be four X squared two x times | |
| 01:17 | three wide . That's six x . Y . And | |
| 01:20 | then three Y times two X . Is also six | |
| 01:24 | X . Y . And finally we have three white | |
| 01:26 | times three which is nine Y squared . Now let's | |
| 01:31 | add the two middle terms 6-plus 6 will give us | |
| 01:36 | 12 . So now we have this expression four X | |
| 01:44 | squared plus 12 X . Y . Plus nine Y | |
| 01:47 | squared . We can see that It's equal to 16 | |
| 01:51 | , which means E . Is the correct answer for | |
| 01:53 | this problem . Number 24 if R squared plus two | |
| 01:59 | R . S Plus S Squared is 81 , then | |
| 02:03 | what is the possible value of R plus S . | |
| 02:10 | So once again we have another perfect square . Try | |
| 02:12 | no meal . And it turns out that R squared | |
| 02:17 | plus two . R . S plus S squared is | |
| 02:20 | R plus S squared . And you could prove it | |
| 02:23 | to yourself . So if we foil these two by | |
| 02:29 | no meals , we're going to get our times are | |
| 02:31 | which is R squared and then our time's S . | |
| 02:35 | And as times are and then S . Times S | |
| 02:39 | . So as we can see this is going to | |
| 02:42 | be the same as what we have here . So | |
| 02:50 | this is still equal to 81 . Our goal is | |
| 02:53 | to get our plus S . So what we need | |
| 02:55 | to do is take the square root of both sides | |
| 02:59 | . The square root of R plus S squared is | |
| 03:02 | R plus S . Now the square root of 81 | |
| 03:06 | . We can get to answers , we can get | |
| 03:08 | plus or -9 , so R plus S . Can | |
| 03:12 | equal nine or R plus S could be negative nine | |
| 03:17 | because if you square nine or negative nine , you | |
| 03:20 | will get 81 . Now positive nine is not one | |
| 03:24 | of the answer choices , but negative nine is so | |
| 03:27 | B is to correct answer 25 . If a squared | |
| 03:33 | plus B squared is equal to our And a plus | |
| 03:37 | B is equal to 8 ? What is the value | |
| 03:40 | of five ? R plus 10 S . Given that | |
| 03:44 | A B C D . S . So we have | |
| 03:46 | a lot of equations here and a lot of variables | |
| 03:50 | . But our goal is to calculate the value Of | |
| 03:53 | five art plus tennis . How can we do that | |
| 04:00 | ? Well , let's write that . What we know | |
| 04:01 | , we know that A squared plus B squared is | |
| 04:05 | our and we know that A times B . S | |
| 04:08 | . We also know that A plus B is eight | |
| 04:13 | . And in this expression we have R and S | |
| 04:17 | . So let's begin by replacing our with a squared | |
| 04:22 | plus B squared . So this is going to be | |
| 04:24 | five times a squared plus B squared . Now let's | |
| 04:30 | replace s with what it equals which is a B | |
| 04:34 | . So this is going to be instead of 10 | |
| 04:36 | s . is going to be 10 times a B | |
| 04:41 | distributed to five . We have five A squared plus | |
| 04:44 | five B squared plus 10 A B . So putting | |
| 04:49 | this in a certain order , notice that we have | |
| 04:52 | a perfect square . Try no meal , I'm going | |
| 04:55 | to factor out five . If I do that , | |
| 04:58 | I'm going to get a squared plus to a B | |
| 05:02 | plus B squared . So in the previous example we | |
| 05:06 | saw that are squared plus two . R . S | |
| 05:09 | plus S squared was just R plus S squared . | |
| 05:13 | Similarly A squared plus two , A B plus B | |
| 05:17 | squared . It's going to be a plus B squared | |
| 05:21 | . Now we have the value of A plus B | |
| 05:24 | . A plus B is eight . So this becomes | |
| 05:26 | five times eight squared , eight squared is 64 . | |
| 05:32 | So now we need to multiply five by 64 . | |
| 05:35 | We know that five times six is 30 , So | |
| 05:38 | five times 60 Is 305 times four is 20 , | |
| 05:43 | so 300 plus 20 Gives Us Street 20 , so | |
| 05:48 | E . Is the correct answer for this problem . |
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