Question

(24+2n) x (24+n) x (24+n) x(2n) = 192 find the value of n​

Answer 1

Step-by-step explanation:

8.1.1 An expression consisting of two terms, connected by + or – sign is called a

binomial expression. For example, x + a, 2x – 3y, 3

1 1 4 , 7

5

x

x x y

− − , etc., are all binomial

expressions.

8.1.2 Binomial theorem

If a and b are real numbers and n is a positive integer, then

(a + b)

n

=nC0

a

n + nC1

a

n – 1 b

1

+ nC2

a

n – 2 b

2

+ ...

... + nCr

a

n – r

br

+ ... + nCn

b

n

, where nCr

=

n

r n r −

for 0 ≤ r ≤ n

The general term or (r + 1)th term in the expansion is given by

Tr + 1 = nCr

a

n–r b

r

8.1.3 Some important observations

1. The total number of terms in the binomial expansion of (a + b)

n

is n + 1, i.e. one

more than the exponent n.

2. In the expansion, the first term is raised to the power of the binomial and in each

subsequent terms the power of a reduces by one with simultaneous increase in

the power of b by one, till power of b becomes equal to the power of binomial,

i.e., the power of a is n in the first term, (n – 1) in the second term and so on

ending with zero in the last term. At the same time power of b is 0 in the first

term, 1 in the second term and 2 in the third term and so on, ending with n in the

last term.

3. In any term the sum of the indices (exponents) of ‘a’ and ‘b’ is equal to n (i.e.,

the power of the binomial).

4. The coefficients in the expansion follow a certain pattern known as pascal’s

triangle.