Transcript binomial expansion –reflection

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 = 32 + 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)= 302 – 52.
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.