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See if you can compute some of these subtractions.
Let's see.
Negative 2 minus minus 45, which is
like adding additive inverse of negative 45, which is 45.
So this subtraction problem turned into negative 2
plus 45, which is 43.
Try that on your own.
So distributive property of multiplication
over subtraction.
What happens when you multiply here?
x times x squared gives me x to the third.
3 times negative 5 will give me negative 15.
So it will be negative 15x to the third.
Negative 4 times negative 5 gives me
positive 20 and x squared.
And then nothing we can do because these are like terms.
So leave it.
Again, distributive property of multiplication
over subtraction.
Negative 2 times 5x cubed.
And then subtract negative 2 times 4x.
And then subtract negative 2 times 6.
Multiplying together, negative 2 times 5 is 10, so 10x cubed.
Negative 2 times 4 is negative 8, and negative of that
would give me 8x because additive inverse.
And here you want additive inverse of negative 12,
which is positive 12.
Go ahead.
Use distributive property on your own,
and see what you can write that as, and then check your answer.
So negative 2 times 4x is negative 8x,
and negative of that would mean additive inverse,
which is positive 8x.
Again, we're using the distributive property
of multiplication over subtraction.
See if you are getting each of those components
or if you're making any mistakes.
3x times 5 will give me 15x.
3x-- 3 times negative 2 is negative 6.
x times x is x squared.
Negative 4 times 5 is negative 20.
Negative 4 times negative 2 is positive 8x.
Then add like terms, so negative 6x squared,
there's nothing to add.
15x plus 8x will give me 23x, and then we have a negative 20.
Fraction subtraction.
What you think we should do?
Same thing that we did with addition, right?
So let's just write our problems,
and see what we can do.
Make equivalent fractions so that they both are
out of the same fraction denominator,
because then we can just add or subtract the numerators.
So first here, we're going to have to multiply that out.
4 times 3 is 12.
4 times negative 4 is negative 16.
Subtracting means additive inverses,
so it's as if there is a negative 1 there,
and you are doing the distribution of multiplication
over subtraction.
So we have 2x minus minus will make it a plus 16x,
so that will make it 18x, and negative 1 times 12
will be negative 12.
It's important that you write everything out
if you're having trouble seeing this
so that you don't make any mistakes.
Same thing here.
Make common denominator, and multiply it out.
So 2 times 3 is 6, 2 times negative a is negative 2a.
Again, there's a little imaginary 1 here
if you have struggling with the negatives.
Negative 1 times 6 is negative 6,
negative 1 times negative 2a is positive 2a.
So this one minus the 6 will give me a negative 5
because you have negative 6 plus 1.
Here we have a negative a, negative 1 times negative 2a,
which will give me positive 2a minus an a
will give me a plus a.
Look very, very carefully, and see
if you understand all the terms.
Negative 1 times 6 is negative 6,
plus 1 gave me the negative 5.
Negative 1 times negative 2a is positive 2a minus the a
will give me a positive a.
If you're having trouble seeing that,
write every single step down.
Do these examples on your own.
So pause the video.
Make sure you're able to do them, because if you get stuck,
then we can help you understand it,
and then you'll see what your mistakes so that you
can do Video Logs on your own.
Let's multiply.
Distribute it out.
So 5x times 2x is 10x squared.
5x times 3 is plus 15x.
x times 2 is 2x.
x times negative x is negative x squared.
Now we're combining like terms.
10x squared minus minus x squared.
Minus minus will make it a plus x squared.
So that's a 1x squared and a 10x squared giving you 11x squared.
15x minus 2x, which will give me 13x.
So that's your final answer.
Let's do the same process here.
Again, distribute it out.
So 3x times x is 3x squared.
3x times 2 is 6x.
2x times 3 is 6x.
2x times negative 4x will be negative 8x squared.
Negative 1 times 3 is negative 3.
Negative 1 times negative 4x is positive 4x.
Now let's combine like terms.
So 3x squared minus minus 8x squared.
We're just adding 8x squared and 3x squared,
giving you 11x squared.
Add the other like terms.
So that's 6x minus 6x, so nothing.
And then minus positive 4x, which
will give you negative 4x.
You see why that is?
6x minus 6x, nothing, zero.
Then you're subtracting a positive 4x,
which will give you a negative 4x.
And minus minus 3, which will give you a plus 3.
Pay very careful attention, and see
if you understand every single item here.
If you're not sure, rewind and watch again
how we're adding and subtracting like terms.
This is your Video Log.