Question

What is the constant term in the expansion of (x + 4)^5?

Answer 1

Final Answer:

The required constant term in the expansion $(x+4)^{5}$ is 1024.

Given:

The given mathematical expression is the expansion $(x+4)^{5}$ .

To Find:

We are required to identify and write the value of the constant term in the expansion $(x+4)^{5}$.

Explanation:

Note that for any binomial expansion of any degree $n$ and containing the only variable $x$ and the only constant $a$ can be expressed by the form $(x+a)^{n}$.

On expanding the expression $(x+a)^{n}$, it is obvious that the only constant term in the whole expansion is only the last term. We can calculate the value of this last term with the expression $a^n$

Step 1 of 2

Since, we are required to find out the constant term only, we will not expand the whole expression.

So identify the following from the given expression.

The variable inside the binomial expression is $=x$.

The constant inside the binomial expression is $=a=4$

Step 2 of 2

So, the required constant term in the expansion $(x+4)^{5}$ is

$=4^5\\=1024$

Therefore, the required constant term in the expansion $(x+4)^{5}$ is 1024.

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https://brainly.in/question/49203696

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