What's up guys? It's Marcus here again.
Today I will be carrying out my very first math tutorial. As you can see,
I've got my equipment prepared and I can't wait to get started.
First, we're gonna start off with expansion where there's only a single bracket. For instance, 5(x+3).
We are going to have to use the "Sign Number Algebra" rule.
5 is positive, so is x. Positive multiplied by positive will yield a positive outcome.
The coefficient of x is 1. 5 multiplied by 1 gives you 5.
The algebraic variable x, will just be written there.
We're gonna do the same process again. Positive multiplied by positive will yield a positive outcome.
5 multiplied by 3 gives you 15. That's the answer.
Here's another one. 2x(7-x).
Let's carry out this process.
Positive multiplied by positive gives you a positive result.
2 multiplied by 7 gives you 14.
I'm gonna bring the algebraic variable right here.
Positive multiplied by negative gives you a negative result.
2 multiplied by 1 gives you 2.
x multiplied by x gives you x squared.
This process, it might seem a little tedious, but it's gonna benefit you
Let's try one more example, which is slightly more difficult.
Consider this.
-3(7-x)+2(x squared-4).
In this example, there are two brackets and you have to
simplify them. What I'm gonna do next is to expand each individual bracket first.
It's gonna be done like this
Negative multiplied by positive gives you negative. 3 multiplied by 7 is 21.
Negative multiplied by negative will give you positive. 3 multiplied by 1 gives you 3 and we bring the x down.
I am going to bring the '+' down.
Positive multiplied by positive will yield a positive outcome.
2 multiplied by 1 is 2.
Bring x squared down. Positive multiplied by negative gives you negative.
2 multiplied by 4 gives you 8. Following that, you rearrange this expression in
descending powers. First, you write 2x squared since it has the highest power,
followed by 3x,
followed by -21 and -8.
These are the constants.
If you simplify it, you're gonna get
2x squared+3x-29. That's my final answer.
What if there are 2 brackets?
Well, let's find out. Let's start with a simple one.
(x+4)(x+3).
We're gonna have to expand and simplify this expression.
The first thing to do is that you have to distribute it bit by bit.
It would be x to x+3 and we're gonna carry out our usual stuff. "Sign Number Algebra".
Positive multiplied by positive will yield a positive outcome. 1 multiplied by 1 gives you 1. x multiplied by x gives you x squared.
Positive multiplied by positive gives you positive.
1 multiplied by 3 gives you 3. I'm gonna bring the x right here. I am gonna do the same for the other distribution.
Positive multiplied by positive yields a positive outcome. 4 multiplied by 1 gives you 4.Bring the x right there.
Positive multiplied by positive gives you a positive outcome and 4 multiplied by 3 gives you 12.
We're gonna simplify the expression.
We get x squared+7x+12.
Let's take it up a notch.
2(3x-5)(x-7).
For this case, I'm gonna deal with these brackets first.
I'm gonna get 2.
We use a different type of bracket.
and expand
Positive multiplied by positive yields a positive outcome. 3 multiplied by 1 gives you 3.
x multiplied by x gives you x squared.
All right!
Positive multiplied by negatives gives you negative.
3 multiplied by 7 gives you 21. Bring the x right there.
Same for this. Negative multiplied by positive yields a negative outcome.
5 multiplied by 1 gives you 5. Bring the x right down.
Negative multiplied by negative gives you a positive result. 5 multiplied by 7 gives you 35.
I'm gonna get 2 bracket 3x squared and simplify this, which gives you -26x plus 35.
All right, I am going to expand this once more
to remove this final bracket.
Positive multiplied by positive gives you a positive result. 2 multiplied by 3 gives you 6. Bring the x squared down.
Positive multiplied by negative gives you negative.
2 multiplied by 26 gives you 52. Bring x down.
Positive multiplied by positive will yield a positive outcome. 2 multiplied by 35 gives you 70.
With that, this is our final answer.
For this final part of the video, we're gonna do expansion.
However, this time some algebraic identities are required. What are these identities?
(a+b) squared. That would give you (a+b)(a+b).
We're gonna distribute it like how we normally do.
You would realise that I get a squared+ab+ab+b squared.
This is the first identity. That is
a squared+2ab+b squared. This is quite essential as it can help you with many things.
It would be good if you can remember this by heart.
Next, (a-b) squared is equivalent to (a-b)(a-b).
We're gonna get a squared-ab-ab+b squared.
That gives you a squared-2ab+ b squared.
We have one more identity.
(a+b)(a-b).
That will give you a squared+ab-ab-b squared.
That is a squared-b squared. This is also known as the difference of squares. This is the most important one.
Let's apply these identities!
All right. For the very first one,
(x+3) squared.
I'm going to use the identity that
(a+b) squared= a squared+2ab+b squared.
If I let a be x and b be 3,
(x) squared+2(x)(3)+(3) squared, where x=a and 3=b.
This gives you x squared+6x+9 and that's the final answer.
Here's another one, (2x-7) squared.
You'll get (2x) squared-2(2x)(7)+(7) squared, where 2x represents a and 7 represents b.
I'm gonna get 4x squared-28x+49.
By the way, this uses a squared-2ab+b squared.
This final one makes use of the identity (a+b)(a-b)= a squared-b squared.
In this case, (7x+2)(7x-2).By using our identity, we get (7x) squared-(2) squared, where 7x represents a and 2 represents b.
We get 49x squared-4.
On that note, the video has ended.
Before I leave, like usual do remember to subscribe and like this video.
If you feel like I can improve in any area , just comment below and I'll get back to that as soon as I can.
