1 00:00:00,419 --> 00:00:02,573 - Which expressions are equivalent 2 00:00:02,573 --> 00:00:06,860 to x plus two-y plus x plus two? 3 00:00:06,860 --> 00:00:09,867 Select all that apply. Alright. 4 00:00:09,867 --> 00:00:13,281 Let's see if I can manipulate this thing a little bit. 5 00:00:13,281 --> 00:00:16,657 Let me just rewrite it so I have x plus... 6 00:00:16,657 --> 00:00:21,611 x plus two-y plus x plus two. 7 00:00:21,611 --> 00:00:23,379 So, the first thing that jumps out at me, 8 00:00:23,379 --> 00:00:24,637 before I even look at these choices, 9 00:00:24,637 --> 00:00:27,299 here I have an x over here, I have an x over there. 10 00:00:27,299 --> 00:00:29,351 Well, if I have one x, and then I can add it to another x 11 00:00:29,351 --> 00:00:32,846 that would be two-x so I could rewrite this... 12 00:00:32,846 --> 00:00:34,350 let me do this in a different color. 13 00:00:34,350 --> 00:00:37,376 I could rewrite this x and this x, 14 00:00:37,376 --> 00:00:40,078 if I add them together that's going to be two-x. 15 00:00:40,078 --> 00:00:43,471 So, this is...actually, I don't want to skip any steps. 16 00:00:43,471 --> 00:00:46,945 So, that's x plus x plus two-y... 17 00:00:46,945 --> 00:00:49,242 now I'm just switching the order...plus two. 18 00:00:49,242 --> 00:00:51,517 And then these two x's right over here, 19 00:00:51,517 --> 00:00:54,220 I can just rewrite that as two-x. 20 00:00:54,220 --> 00:00:57,575 So, I have two-x plus two-y... 21 00:00:57,575 --> 00:01:00,955 plus two-y plus two. 22 00:01:00,955 --> 00:01:03,240 Now, let's see, out of all my choices... 23 00:01:03,240 --> 00:01:05,767 so, this one, 24 00:01:05,767 --> 00:01:10,247 this is two-x plus four-y plus four. 25 00:01:10,247 --> 00:01:13,581 So, that's not right, I have two-x plus two-y plus 2, 26 00:01:13,581 --> 00:01:15,247 so I can rule this one out. 27 00:01:15,247 --> 00:01:16,871 Now, this one's interesting, it looks like 28 00:01:16,871 --> 00:01:17,950 they have factored out a two. 29 00:01:17,950 --> 00:01:20,509 Let's see if we factor out a two here, what happens? 30 00:01:20,509 --> 00:01:22,642 So, we do see that two is a factor of that term, 31 00:01:22,642 --> 00:01:25,507 it's a factor of that term, and it's a factor of that term. 32 00:01:25,507 --> 00:01:28,717 So, let's see if we can factor it out. 33 00:01:28,717 --> 00:01:32,516 So, this is going to be two times x, 34 00:01:32,516 --> 00:01:37,373 I'll do the x in that same magenta color, two times x plus, 35 00:01:37,373 --> 00:01:40,847 we have just a y left when you factor out the two. 36 00:01:40,847 --> 00:01:42,350 And then if you factor out a two here, 37 00:01:42,350 --> 00:01:43,895 you're just going to have a one left. 38 00:01:43,895 --> 00:01:46,983 So, two times x plus y plus one. 39 00:01:46,983 --> 00:01:49,705 Which is exactly what they have over here. 40 00:01:49,705 --> 00:01:51,513 And since I was able to find a choice, 41 00:01:51,513 --> 00:01:56,355 I will not pick "None of the above".