Binomial Theorem Coefficient of x^6 in (x-2)^12

Published on April 26, 2026

Algebra

Learn how to use the Binomial Theorem to find the coefficient of x^6 in the expansion of (x-2)^12. This involves calculating binomial coefficients and powers.

Question

Use the Binomial Theorem to find the coefficient of x Superscript 6 in the expansion of left parenthesis x minus 2 right parenthesis Superscript 12 Baseline . Question content area bottom Part 1 enter your response herex Superscript 6

Answer

The Binomial Theorem states that for any non-negative integer

, the expansion of

is given by:

where

is the binomial coefficient.

In this problem, we need to find the coefficient of

in the expansion of

.
Here,

, and

We are looking for the term where the power of

. In the general term

, the power of

(which is

in our case) is

.
So, we need to find the value of

such that

.
Given

, we have:

Subtracting

from both sides:

Multiplying by

Now we substitute

, and

into the general term of the Binomial Theorem:
The term is

First, calculate the binomial coefficient

Next, calculate

Now, combine the parts to find the term with

:
Term =

The coefficient of

Therefore, the coefficient of

in the expansion of

The final answer is

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