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## SAT (Fall 2023)

### Course: SAT (Fall 2023) > Unit 10

Lesson 2: Passport to advanced mathematics- Solving quadratic equations — Basic example
- Solving quadratic equations — Harder example
- Interpreting nonlinear expressions — Basic example
- Interpreting nonlinear expressions — Harder example
- Quadratic and exponential word problems — Basic example
- Quadratic and exponential word problems — Harder example
- Manipulating quadratic and exponential expressions — Basic example
- Manipulating quadratic and exponential expressions — Harder example
- Radicals and rational exponents — Basic example
- Radicals and rational exponents — Harder example
- Radical and rational equations — Basic example
- Radical and rational equations — Harder example
- Operations with rational expressions — Basic example
- Operations with rational expressions — Harder example
- Operations with polynomials — Basic example
- Operations with polynomials — Harder example
- Polynomial factors and graphs — Basic example
- Polynomial factors and graphs — Harder example
- Nonlinear equation graphs — Basic example
- Nonlinear equation graphs — Harder example
- Linear and quadratic systems — Basic example
- Linear and quadratic systems — Harder example
- Structure in expressions — Basic example
- Structure in expressions — Harder example
- Isolating quantities — Basic example
- Isolating quantities — Harder example
- Function notation — Basic example
- Function notation — Harder example

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# Operations with polynomials — Harder example

Watch Sal work through a harder Operations with polynomials problem.

## Want to join the conversation?

- why couldn't he just do 1/88 - 1/44 and have gotten d as his answer?(12 votes)
- (1/88)-(1/44) would be equal to -(1/88) because 1/44 is equal to 2/88 so it would technically be (1/88)-(2/88) 1-2 = -1 overall equaling -1/88(7 votes)

- There is only one possible answer. The others are not even close!(10 votes)
- exactly. But even if it isn't close, there r ways to get the wrong answers accidentally.(3 votes)

- If I can do the problem in my head, should I trust my abilities or still try to write down some work?(4 votes)
- Well, if you have some time left, you should write down. This will confirm whether the answer is correct or not. If you are running out of time, trust your abilities.(5 votes)

- It's just me or this one is so much easier than the basic example?(5 votes)
- lol this is easier than the basic(5 votes)
- At1:21why do the two y^100s become one?(2 votes)
- We have (1/88)*y^100+(-1/44*y^100) +3/2

so now we are going to add (in this case subtract because the second term is negative) both the like terms i.e (y^100)/88 and (-y^100)/44

The LCM is 88

we get (y-2y)/88

at this point do not forget the 3/2 we have to add

so we get

(-y^100)/88+3/2

which can also be written as

(-1/88)*y^100 + 3/2

which is option 2

Hope this helped you:)(6 votes)

- Why didn't he see the -ve coefficient coming ASAP?(3 votes)
- I'm still kind of confused(3 votes)
- does anyone have some other tips and advice to prepare for the SAT other than Khan Academy?(2 votes)
- Yeah, there are many online sites that provide tips, one that I would suggest is PrepScholar Blogs.(2 votes)

- What happens if there is a negative number under the root?(2 votes)
- Since number under the square is a^2, there can't be. Let me explain a bit.

If "a" is positive: positive x positive = positive

If "a" is negative: negative x negative = negative

So there is no scenario of a negative number being under the root if we do not use imaginary numbers. It would be possible if we used imaginary numbers. for example: i^2 = -1 so i = -1 under the root. :)(1 vote)

## Video transcript

- [Instructor] Which of
the following expressions is equivalent to 7k, 7k, minus, minus the product of k
plus 1 and 2k plus 2? All right. So this is going to be 7k minus, 7k minus the product of
k plus one and 2k plus 2. And, so let's see. To kind of expand it all out, we will want to multiply
these two expressions, so let's do that first. So it's going to be, this
is going 7k minus, minus, and then let's just multiply this out. You're gonna have k times
2k, which is 2k squared, k times 2, which is gonna be plus 2k, then 1 times 2k, which is
going to give us another 2k, and then 1 times 2, which
is going to give us plus 2. So, and we want to be careful. We want to put a parentheses out front 'cause we're gonna
subtract all of this stuff right over here. So this is going to be
the same as 7k minus, 7k minus, and then in
parentheses, we have 2k squared. We can add 2k plus 2k to
get 4k, plus 4k plus 2. And now we can, one way
to think about it is we can distribute this negative sign, or you could even view this
as minus 1 times all of this. And so this is going to be the same this 7k minus 2k squared, so minus 2k squared, 2k squared, minus 4k, minus 4k, and then minus 2, minus 2. And let's see. So if we write the
highest degree term first, if we write this term, let me do this in a different color, if we were to write this term first, you get negative 2k squared,
that's our highest degree term, and actually immediately
when you look at the choices, only one of these start
with negative 2k squared. It has negative 2 as the
coefficient on the k squared term. So we already know that that
one's going to be the choice, but let's just confirm it. So it's negative 2k squared,
and then we could add, we could add 7k and negative 4k. Those two are going to add, 7 minus 4, so I'm thinking it's
gonna be three of that, so it's gonna be plus 3k, which is what we see right over there. And then finally, you hae
this minus 2, minus 2, which is exactly what we see
in this first choice up here.