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Expand the expression (1– 2x)5
By using Binomial Theorem, the expression (1– 2x)5 can be expanded as
Expand the expression
By using Binomial Theorem, the expression can be expanded as
Expand the expression (2x – 3)6
By using Binomial Theorem, the expression (2x – 3)6 can be expanded as
Expand the expression
By using Binomial Theorem, the expression can be expanded as
Using Binomial Theorem, evaluate (96)3
96 can be expressed as the sum or difference of two numbers whose powers are easier to calculate and then, binomial theorem can be applied.
It can be written that, 96 = 100 – 4
Using Binomial Theorem, evaluate (102)5
102 can be expressed as the sum or difference of two numbers whose powers are easier to calculate and then, Binomial Theorem can be applied.
It can be written that, 102 = 100 + 2
Using Binomial Theorem, evaluate (101)4
101 can be expressed as the sum or difference of two numbers whose powers are easier to calculate and then, Binomial Theorem can be applied.
It can be written that, 101 = 100 + 1
Using Binomial Theorem, evaluate
99 can be written as the sum or difference of two numbers whose powers are easier to calculate and then, Binomial Theorem can be applied.
It can be written that, 99 = 100 – 1
Using Binomial Theorem, indicate which number is larger (1.1)10000 or 1000.
By splitting 1.1 and then applying Binomial Theorem, the first few terms of (1.1)10000 can be obtained as
Find (a + b)4 – (a – b)4. Hence, evaluate
.
Using Binomial Theorem, the expressions, (a + b)4 and (a – b)4, can be expanded as
Find (x + 1)6 + (x – 1)6. Hence or otherwise evaluate
.
Using Binomial Theorem, the expressions, (x + 1)6 and (x – 1)6, can be expanded as
By putting
, we obtain
Show that 
is divisible by 64, whenever n is a positive integer.
In order to show that is divisible by 64, it has to be proved that,
, where k is some natural number
By Binomial Theorem,
For a = 8 and m = n + 1, we obtain
Thus, is divisible by 64, whenever n is a positive integer.
Prove that
.
By Binomial Theorem,
By putting b = 3 and a = 1 in the above equation, we obtain
Hence, proved.
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