# BINOMIAL EXPANSION – REFLECTION BY: KHALIFA AL THANI.

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BINOMIAL EXPANSION – REFLECTION BY: KHALIFA AL THANI

USES OF ALGEBRIC FORMULA INSTEAD OF LONG MULTIPLICATION

As I am an engineer I have to do lot of calculations involving multiplication and I would have wasted lot of time for doing long multiplication. It is very clear that if I want to find area of a square room with 3.5 mts. in length I have to do the algebraic formula in the following way.

(3 + 0.5)2 = 3 2 + 2x5x (0.5) + (o.5)2 = 9+ 5+0.25 = 14.25 m2

Where as when we multiply 3.5 with 3.5 it is time wasting process. In olden days lot of calculation errors also were there when we do long multiplication without using the formulas.

When there is more than two decimal places our method will be very tough. Because it will be as same as the multiplication done manually. consider the example 5.008 x 5.008 (5 + 0.008)2 = 52 + 2x5x (0.008) + (o.008)2

Here we have to multiply again 0.008 manually.Therefore in this type of numbers with more decimals our method is not so good and it makes our work double.

Consider the examples like 10000 x10000 …..here we are feeling so comfort to multiply directly. But if we are using the formula here we have to make it as either (9999 + 1)2 or (10001 - 1)2 …this both method will be very hard for us.

In general we have to look at the number and we have to think the comfort in multiplication. if want to find 49x49 it is very easy. we can use (50 - 1)2 as the square of 50 and 1 are easily known to us the calculation will be done faster.

Here are some products which we can use the algebraic identity. 99x99= (100- 1)2 101x101=(100 + 1)2 When the numbers are so big or it involves more number of decimals say more than three decimals long multiplication is easy.

Similarly number following some pattern also can be used by algebraic identity Consider the product 35x25 we can use a2 - b2 = ( a + b )( a - b) here we are taking it as ( 30 + 5 )( 30 - 5)= 30 2 – 5 2.

In short we can say that many cases this can be done without any problems but some case long multiplication will be very useful. Main important idea is we can use the algebraic formula to verify our result which obtained after long multiplication.