Question

# Use binomial theorem to expand

## The correct answer is: 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.

### ANSWER:

Hint:

The binomial expansion is , here .

We are asked to use binomial theorem to expand

Step 1 of 2:

The given expression is , where .Here, the value of n=6, hence we would have 6+1=7 terms in the expression.

Step 2 of 2:

Substitute the values of in the binomial expression;

Thus, the expansion is:

Note:

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.

### Related Questions to study

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### How are Pascal’s triangle and binomial expansion such as (a + b)^{5} related?

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### Explain why the middle term is 10x.

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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.

### Explain why the middle term is 10x.

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.

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

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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.

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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.

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