Question

What is the coefficient of the x^4 term in the expanded form of (2x-7)^6

Answer 1

The coefficient of
`x^(4)` = 11760

Explanation:

∵ The rule of expanded the binomial is :

`(a+b)^(n)=C_(0) ^(n) a^(n)b^(0)+C_(1)^(n)a^(n-1)b^(1)+C_(2)^(n)a^(n-2)b^(2)+.............`

∴ The Expanded of
`(2x-7)^(6)` is:

`(2x-7)^(6)=C_(0)^(6)(2x)^(6)(-7)^(0)+C_(1)^(6)(2x)^(5)(-7)^(1)+C_(2)^(6)(2x)^(4)(-7)^(2)+..........`

`(2x-7)^(6)=(1)(64x^(6))(1)+(6)(32x^(5))(-7)+(15)(16x^(4))(-7)^(2)`

We will take the term of
`x^(4)` and find the coefficient of it

∴ The coefficient of
`x^(4)` =
`(15)(16)(-7)^(2)=(15)(16)(49)=11760`