Question

Find the coefficient of third term of (2x−1)^6.

Answer 1

240

using pascals trianle

for the power 6 it is

1, 6,15,20, 15,6, 1

and for the third term (2x)^4 and (-1)^2

$15 \times {(2x)}^{4} \times {( - 1)}^{2}$

$240 {x}^{4}$

Since only the coefficient is needed

the answer is 240.

Answer 2

The required coefficient of third term is 480.

Coefficient of the third term of (2x−1)^6 to be determine.

What is coefficient?

Coefficient is defined as the integer present adjacent to the variable.

Here,  (2x−1)^6
Using binomial expansion,
Third term = P(6,2)(2x)^6-2(-1)^2
                  =   6*5*16x^4
                  = 480x^4

Thus, the required coefficient of third term is 480.

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