Algebraic identities 🤟🏼....

 Hello again curious minds .....

 Hope you have tried all the questions which I had given in the previous blog and in case if not done then go back and must try as it will help you to check your understanding of concept......

So, now let's learn some algebraic identities which will help to solve the big calculations in a short and simple way and also it will take less time.....

May be you are familiar with these identities, if yes then just see it once so that it will get refreshes.....
And also we will see it's benefits in solving the problems by taking some examples......

Let's first list out all identities...

We will not list out it normally ,let's make little colorful and attractive by using  CANVA 🤟🏼....

Just try to memorize these identities or also we can learn it with the help of binomial theorem and also by diagram....

Binomial theorem - 

Let's see how we can use binomial theorem to learn the identities by taking one or two samples......

As you can see the expansion of the theorem so let's start to apply it .....

1.  For finding (a+b)²  we put x=a, y=b and n=2 in the above expansion so it will become

(a+b)² = ²Co a² b⁰ + ²C1 a¹ b¹ + ²C2 a⁰ b²

= a² + 2ab + b²

As the value of  :

²Co = 1 = ²C2  and  a⁰ = 1 = b⁰ 

2.  For finding  (a+b)³ it will be written as 

(a+b)³ = ³Co a³ b⁰ + ³C1 a² b¹

              + ³C2 a¹ b² + ³C3 a⁰ b³

            

               = a³ + 3 a²b + 3 ab² + b³

As the value of  :

³Co = 1 = ³C3 , ³C1 = 3 = ³C2  and   a⁰ = b ⁰ = 1

Likewise you can also try to find other identities through the above binomial theorem expansion.......

Above are the two ways to learn the identities...

Now let's take one example for better understanding ...

Evaluate -> (x + 3) (x + 3) 

So by using identity (a+b)², we can solve it easily and quickly, 

 (x + 3)²  = x²+ 2(x)(3) + (3)²

      = x² + 6 x + 9

Let me give you some problems so that you can check your understanding and solve these by using identities......

               1.     Expand ->  (4 a – 2 b – 3 c)²

2.     Evaluate ->  (104)³

3.     Evaluate ->  (999)³

      4.     Solve ->  (x + 4) (x + 10)

                    5.     Solve -> (67.542)² - (32.458)²

                                            75.458 - 40.374

Must try these questions as it will test your knowledge and understanding about the above information........

And if you find any difficulty, comment below 👇🏼......

Hope you will try these questions.......