Math Lesson 12.3.6 - What is a Binomial when it is not in the Standard Form

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Welcome to our Math lesson on What is a Binomial when it is not in the Standard Form, this is the sixth lesson of our suite of math lessons covering the topic of Binomial Expansion and Coefficients, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

Working with a Binomial when it is not in Standard Form

When a binomial is not expressed in the standard form, first we try to write it in the standard form before continuing with the normal procedure. For example, in the expression

first, we make the necessary simplifications before continuing with the rest, i.e.

Next, we express 2x = a and -y = b. Hence, given that

we obtain after the substitutions

Example 5

What is the expanded form of

Solution 5

First, we simplify the expression in the brackets to turn it into a binomial. We have

We express 4x as a and -2 as b. Thus, we obtain

Replacing back a and b with the original terms yields

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