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Chapter 8: Problem 63

How do you determine how many terms there are in a binomial expansion?

Short Answer

Expert verified
The number of terms in a binomial expansion is given by \(n+1\), where 'n' is the power to which the binomial expression is raised.

Step by step solution

01

Understand Binomial Expansion

A binomial is an algebraic expression of the sum or the difference of two terms. Binomial expansion refers to expanding an expression that is raised to a power, in its potential series of terms. The power to which the binomials are raised is extremely relevant here.
02

Understand the Binomial Theorem

The Binomial Theorem tells us how to expand a binomial expression that is raised to a power. It is given by: \((a + b)^n = a^n + ^nC_1 * a^{n-1} * b + ^nC_2 * a^{n-2} * b^2 + ^nC_3 * a^{n-3} * b^3 + ... + b^n \) From the above formula, it is visible that the number of terms in the expansion can be found by easily counting the terms.
03

Finding the Number of terms

The number of terms in a binomial expression's expansion is given by \(n+1\), where 'n' is the power to which the binomial expression is raised. For instance, if we are asked to find the number of terms in the expansion of \((x+y)^5\), according to our understanding, the number of terms would be \('n+1'\) =5+1=6. So, the number of terms in the expansion of \((x+y)^5\) will be 6.

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