Question

# Explain why the middle term is 10x.

Hint:

### The binomial expansion is , here n ≥ 0 . We are asked to explain why the middle term (x + 5)2 is 10x.

## The correct answer is: = x2 + 10x + 25

Step 1 of 1:

The given expression is: (x + 5)^{2}

Here, a=x and b=5.

Here, the middle term is 10x because while expanding you have the form,

In the Binomial Expansion's middle term, in the expansion of (a + b)n, there are (n + 1) terms. Therefore, we can write the middle term or terms of (a + b)n based on the value of n. It follows that there will only be one middle term if n is even and two middle terms if n is odd.

The binomial expansions of (x + y)n are used to find specific terms, such as the term independent of x or y.

Practice Questions

1. Find the expansion of (9x - 2y)12's coefficient of x5y7.

2. In the expansion of (2x - y)11, locate the 8th term.

### Related Questions to study

### Use binomial theorem to expand .

### Use binomial theorem to expand .

### Use polynomial identities to factor the polynomials or simplify the expressions :

### Use polynomial identities to factor the polynomials or simplify the expressions :

### How can you use polynomial identities to rewrite expressions efficiently ?

Polynomial identities are equations that are true for all possible values of the variable and numbers.

### How can you use polynomial identities to rewrite expressions efficiently ?

Polynomial identities are equations that are true for all possible values of the variable and numbers.

### Use binomial theorem to expand (2c + d)^{6}

The expansion of the expression can also be found using the Pascal’s triangle. But, it is necessary to remember the values of the triangle to write down the expansion.

### Use binomial theorem to expand (2c + d)^{6}

The expansion of the expression can also be found using the Pascal’s triangle. But, it is necessary to remember the values of the triangle to write down the expansion.

### Use binomial theorem to expand .

### Use binomial theorem to expand .

### Use binomial theorem to expand (x - 1)^{7}

For the expansion of an expression (x + y)n , we would have n+1 terms. This is something you need to keep in mind.

### Use binomial theorem to expand (x - 1)^{7}

For the expansion of an expression (x + y)n , we would have n+1 terms. This is something you need to keep in mind.

### Use polynomial identities to factor the polynomials or simplify the expressions :

### Use polynomial identities to factor the polynomials or simplify the expressions :

### Use Pascal triangle to expand

### Use Pascal triangle to expand

### Use binomial theorem to expand (s^{2} + 3)^{5}

For the expansion of an expression (x + y)n , we would have n+1 terms. This is something you need to keep in mind.