Question

what is the coffiecent of x in expansion of x+2^2

Answer 1

Answer:

in (x+2)^2, the coefficient of x is 4.

and in x+2^2, i.e. x+4, the coefficient of x is 1.

Answer 2

Answer:

The answer will be 4x.

Step-by-step explanation:

Here we go,

We need to expland:

${(x + 2)}^{2}$

There are two ways to do it.

(i) The power isn't very high so just break it on the a+b whole squared format and take 2×2 as the coefficient.

(ii)Do a proper binomial expansion:

To get the required coefficient we must set the power to 1.

So,

Let term with coefficient x

Since,

t(r+1) = {nCr}{a^r}{b^(n-r)}

Where a and b are the terms of the binomial,

here

r =0 So that x could've been 1.

t(1) = {2C0} (x)^1{2^(2-0)}

t(1) = (2!/2!)(x)(2^2) = x(4) = 4x.

Hence your answer.