[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:01.10,0:00:03.79,Default,,0000,0000,0000,,Simplify: negative one times this expression in brackets
Dialogue: 0,0:00:03.79,0:00:07.39,Default,,0000,0000,0000,,negative seven plus 2 times 3 plus 2
Dialogue: 0,0:00:07.39,0:00:11.11,Default,,0000,0000,0000,,minus 5 in parentheses, squared.
Dialogue: 0,0:00:11.11,0:00:14.00,Default,,0000,0000,0000,,So this is an order of operations problem,
Dialogue: 0,0:00:14.00,0:00:16.46,Default,,0000,0000,0000,,and remember in order of operations,
Dialogue: 0,0:00:16.46,0:00:18.53,Default,,0000,0000,0000,,you always wanna do parentheses first.
Dialogue: 0,0:00:18.53,0:00:20.21,Default,,0000,0000,0000,,Parentheses.
Dialogue: 0,0:00:20.21,0:00:22.36,Default,,0000,0000,0000,,Parentheses..first.
Dialogue: 0,0:00:22.36,0:00:25.57,Default,,0000,0000,0000,,Then you do exponents. Exponents.
Dialogue: 0,0:00:25.57,0:00:29.09,Default,,0000,0000,0000,,And there are--there is an exponent in this problem, right over here.
Dialogue: 0,0:00:29.09,0:00:31.24,Default,,0000,0000,0000,,Then you wanna do multiplication...
Dialogue: 0,0:00:31.24,0:00:33.54,Default,,0000,0000,0000,,multiplication and division,
Dialogue: 0,0:00:33.54,0:00:37.57,Default,,0000,0000,0000,,and then finally you do addition and subtraction.
Dialogue: 0,0:00:37.57,0:00:40.20,Default,,0000,0000,0000,,So let's just try to tackle this as best we can.
Dialogue: 0,0:00:40.20,0:00:44.84,Default,,0000,0000,0000,,So first let's do the parentheses. Let's do the parentheses...
Dialogue: 0,0:00:44.84,0:00:47.52,Default,,0000,0000,0000,,We have a 3+2 here in parentheses,
Dialogue: 0,0:00:47.52,0:00:51.22,Default,,0000,0000,0000,,so we can evaluate that to be equal to 5.
Dialogue: 0,0:00:51.22,0:00:55.04,Default,,0000,0000,0000,,And let's see we can do other things in other parts of this expression
Dialogue: 0,0:00:55.04,0:00:57.95,Default,,0000,0000,0000,,that won't affect what's going on right here in the parentheses.
Dialogue: 0,0:00:57.95,0:01:01.18,Default,,0000,0000,0000,,We have this negative 5 squared,
Dialogue: 0,0:01:01.18,0:01:03.92,Default,,0000,0000,0000,,or actually I should say we have some subtracting of 5 squared.
Dialogue: 0,0:01:03.92,0:01:07.68,Default,,0000,0000,0000,,We wanna do the exponent before we worry about being subtracted,
Dialogue: 0,0:01:07.68,0:01:12.77,Default,,0000,0000,0000,,so this 5 squared over here, we can rewrite as 25.
Dialogue: 0,0:01:12.77,0:01:15.61,Default,,0000,0000,0000,,Let's not do too many steps at once,
Dialogue: 0,0:01:15.61,0:01:18.43,Default,,0000,0000,0000,,so this whole thing would simplify to negative 1,
Dialogue: 0,0:01:18.43,0:01:24.18,Default,,0000,0000,0000,,and then in brackets we have negative 7 plus 2 times 5,
Dialogue: 0,0:01:24.18,0:01:29.47,Default,,0000,0000,0000,,plus 2 times 5, and then 2 times 5,
Dialogue: 0,0:01:29.47,0:01:32.43,Default,,0000,0000,0000,,and close brackets, minus 25.
Dialogue: 0,0:01:32.43,0:01:34.90,Default,,0000,0000,0000,,Minus 25.
Dialogue: 0,0:01:34.90,0:01:38.83,Default,,0000,0000,0000,,Now, this thing we wanna do multiplication.
Dialogue: 0,0:01:38.83,0:01:39.75,Default,,0000,0000,0000,,You could say,
Dialogue: 0,0:01:39.75,0:01:41.99,Default,,0000,0000,0000,,"hey, we have the parentheses, why don't we do them first"
Dialogue: 0,0:01:41.99,0:01:44.07,Default,,0000,0000,0000,,but when we just evaluate what's inside these parentheses
Dialogue: 0,0:01:44.07,0:01:45.42,Default,,0000,0000,0000,,you just get a negative 7,
Dialogue: 0,0:01:45.42,0:01:46.74,Default,,0000,0000,0000,,it doesn't really change anything.
Dialogue: 0,0:01:46.74,0:01:48.90,Default,,0000,0000,0000,,So we can just leave this as negative 7.
Dialogue: 0,0:01:48.90,0:01:52.09,Default,,0000,0000,0000,,And this expression, we do want to evaluate this whole expression
Dialogue: 0,0:01:52.09,0:01:53.67,Default,,0000,0000,0000,,before we anything else.
Dialogue: 0,0:01:53.67,0:01:55.99,Default,,0000,0000,0000,,I mean we could distribute this negative 1 and all that,
Dialogue: 0,0:01:55.99,0:01:58.79,Default,,0000,0000,0000,,but let's just do straight up order of operations here.
Dialogue: 0,0:01:58.79,0:02:00.62,Default,,0000,0000,0000,,So let's evaluate this expression.
Dialogue: 0,0:02:00.62,0:02:03.44,Default,,0000,0000,0000,,We want to do multiplication before we add anything.
Dialogue: 0,0:02:03.44,0:02:06.27,Default,,0000,0000,0000,,So we get a 2 times 5 right over there,
Dialogue: 0,0:02:06.27,0:02:10.14,Default,,0000,0000,0000,,2 times 5 is 10. That is 10.
Dialogue: 0,0:02:10.14,0:02:11.95,Default,,0000,0000,0000,,So our whole expression becomes...
Dialogue: 0,0:02:11.95,0:02:14.28,Default,,0000,0000,0000,,Normally you don't have to rewrite the expression this many times,
Dialogue: 0,0:02:14.28,0:02:15.72,Default,,0000,0000,0000,,but what we're gonna do at this time
Dialogue: 0,0:02:15.72,0:02:17.56,Default,,0000,0000,0000,,to make sure no one gets confused.
Dialogue: 0,0:02:17.56,0:02:23.32,Default,,0000,0000,0000,,So is becomes negative 1 times negative 7 plus 10,
Dialogue: 0,0:02:23.32,0:02:31.81,Default,,0000,0000,0000,,plus 10, we close our brackets, minus 25. Minus 25.
Dialogue: 0,0:02:31.81,0:02:34.37,Default,,0000,0000,0000,,Now we can evaluate this pretty easily.
Dialogue: 0,0:02:34.37,0:02:39.38,Default,,0000,0000,0000,,Negative 7 plus 10. You can view as starting with negative 7,
Dialogue: 0,0:02:39.38,0:02:41.98,Default,,0000,0000,0000,,so I was gonna draw a number line there.
Dialogue: 0,0:02:41.98,0:02:45.61,Default,,0000,0000,0000,,So we're starting - draw a number line -
Dialogue: 0,0:02:45.61,0:02:48.45,Default,,0000,0000,0000,,so we're starting at negative 7 and then...
Dialogue: 0,0:02:48.45,0:02:51.36,Default,,0000,0000,0000,,- so this, the length of the line is negative 7 -
Dialogue: 0,0:02:51.36,0:02:53.18,Default,,0000,0000,0000,,... and then we're adding 10 to it.
Dialogue: 0,0:02:53.18,0:02:55.53,Default,,0000,0000,0000,,We are adding 10 to it.
Dialogue: 0,0:02:55.53,0:02:57.01,Default,,0000,0000,0000,,So we're going to move 10 to the right.
Dialogue: 0,0:02:57.01,0:02:58.78,Default,,0000,0000,0000,,If we move 7 to the right we get back to 0,
Dialogue: 0,0:02:58.78,0:03:02.63,Default,,0000,0000,0000,,and then we're going to go another 3 after that.
Dialogue: 0,0:03:02.63,0:03:05.44,Default,,0000,0000,0000,,So we're gonna go 7, 8, 9, 10.
Dialogue: 0,0:03:05.44,0:03:08.09,Default,,0000,0000,0000,,So gets us to positive 3.
Dialogue: 0,0:03:08.09,0:03:10.55,Default,,0000,0000,0000,,Another way to think about it is,
Dialogue: 0,0:03:10.55,0:03:13.94,Default,,0000,0000,0000,,we are adding integers of different signs,
Dialogue: 0,0:03:13.94,0:03:18.58,Default,,0000,0000,0000,,we can view this sum as going to be
Dialogue: 0,0:03:18.58,0:03:20.35,Default,,0000,0000,0000,,the difference of the integers,
Dialogue: 0,0:03:20.35,0:03:23.21,Default,,0000,0000,0000,,and since our larger integer is positive,
Dialogue: 0,0:03:23.21,0:03:25.21,Default,,0000,0000,0000,,the answer will be positive.
Dialogue: 0,0:03:25.21,0:03:27.73,Default,,0000,0000,0000,,So you could literally just view this as 10 minus 7.
Dialogue: 0,0:03:27.73,0:03:29.86,Default,,0000,0000,0000,,10 minus 7 is 3.
Dialogue: 0,0:03:29.86,0:03:34.80,Default,,0000,0000,0000,,So this becomes a 3, so the entire expression becomes negative 1.
Dialogue: 0,0:03:34.80,0:03:37.46,Default,,0000,0000,0000,,Negative 1 times...
Dialogue: 0,0:03:37.46,0:03:38.63,Default,,0000,0000,0000,,- and just to be clear:
Dialogue: 0,0:03:38.63,0:03:40.96,Default,,0000,0000,0000,,brackets and parentheses are really the same thing
Dialogue: 0,0:03:40.96,0:03:43.83,Default,,0000,0000,0000,,Sometimes people will write brackets around a lot of parentheses
Dialogue: 0,0:03:43.83,0:03:45.78,Default,,0000,0000,0000,,just to make it a little bit easier to read,
Dialogue: 0,0:03:45.78,0:03:47.98,Default,,0000,0000,0000,,but they are really just the same thing as parentheses.
Dialogue: 0,0:03:47.98,0:03:49.40,Default,,0000,0000,0000,,So these brackets are here,
Dialogue: 0,0:03:49.40,0:03:51.73,Default,,0000,0000,0000,,I could just literally write them like that.
Dialogue: 0,0:03:51.73,0:03:56.02,Default,,0000,0000,0000,,And then I have a minus 25 out over here.
Dialogue: 0,0:03:56.02,0:03:58.59,Default,,0000,0000,0000,,Now once again you wanna do multiplication or division
Dialogue: 0,0:03:58.59,0:04:00.11,Default,,0000,0000,0000,,before we do addition and subtraction,
Dialogue: 0,0:04:00.11,0:04:02.80,Default,,0000,0000,0000,,so it's multiplied the negative 1 times 3,
Dialogue: 0,0:04:02.80,0:04:04.65,Default,,0000,0000,0000,,is negative 3.
Dialogue: 0,0:04:04.65,0:04:07.23,Default,,0000,0000,0000,,And now we need to subtract our 25.
Dialogue: 0,0:04:07.23,0:04:10.21,Default,,0000,0000,0000,,So negative 3 minus 25,
Dialogue: 0,0:04:10.21,0:04:13.06,Default,,0000,0000,0000,,we are adding two integers of the same sign.
Dialogue: 0,0:04:13.06,0:04:14.63,Default,,0000,0000,0000,,We are already at negative 3,
Dialogue: 0,0:04:14.63,0:04:16.59,Default,,0000,0000,0000,,it will become 25 more negative than that.
Dialogue: 0,0:04:16.59,0:04:18.94,Default,,0000,0000,0000,,So you can view this as...
Dialogue: 0,0:04:18.94,0:04:22.16,Default,,0000,0000,0000,,we are moving 25 more in the negative direction.
Dialogue: 0,0:04:22.16,0:04:24.48,Default,,0000,0000,0000,,Or you can view this as 3 plus 25 is 28,
Dialogue: 0,0:04:24.48,0:04:26.15,Default,,0000,0000,0000,,we're doing it in the negative direction,
Dialogue: 0,0:04:26.15,0:04:27.96,Default,,0000,0000,0000,,so it's negative 28.
Dialogue: 0,0:04:27.96,0:04:33.17,Default,,0000,0000,0000,,So this is equal to negative 28.
Dialogue: 0,0:04:33.17,0:04:34.71,Default,,0000,0000,0000,,And we are done!