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Binomial Theorem

Exercises in expanding powers of binomial expressions and finding specific coefficients.
Brackets Pascal's Triangle Level 1 Level 2 Exam-Style Description Help More Algebra

This is level 1: complete expansions of binomials

Use the ^ key to type in a power or index and use the forward slash / to type a fraction. Press the right arrow key to end the power or fraction.

1. Expand \( (a+b)^3\) in descending powers of \(a\)

Correct Wrong

2. Expand \( (x+2)^4\) in descending powers of \(x\)

Correct Wrong

3. Expand \( (2x+3y)^5\) in descending powers of \(x\)

Correct Wrong

4. Expand \( (c-d)^6\) in descending powers of \(c\)

Correct Wrong

5. Expand \( (x-3)^4\) in descending powers of \(x\)

Correct Wrong

6. Expand \( (2w-3)^5\) in descending powers of \(w\)

Correct Wrong

7. Give the first 3 terms of the expansion of \( (2j+5k)^7\) in descending powers of \(j\)

Correct Wrong

8. Give the last 3 terms of the expansion of \( (3e-2f)^6\) in descending powers of \(e\)

Correct Wrong

9. Expand \( (3x+ \frac{y}{2})^3\) in descending powers of \(x\)

Correct Wrong

10. Expand \( (4x-\frac{1}{2x})^5\) in descending powers of \(x\)

Correct Wrong
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This is Binomial Theorem level 1. You can also try:
Level 2

Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.
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Description of Levels

Brackets - The basics of expanding brackets

Pascal's Triangle - See how the coefficients are generated

Level 1 - Complete expansions of binomials

Level 2 - Finding specific coefficients

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

More Algebra including lesson Starters, visual aids, investigations and self-marking exercises.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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Binomial Theorem Revision

Using a Scientific Calculator

The function to work out a number in Pascal's Triangle appears as nCr where:

nCr Formula nCr button on calculator

Using a Graphic Display Calculator

With a GDC you can work out a whole row of Pascal's Triangle using the combinations function. Here is a screenshot of the TI Nspire.

Combinations function

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

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Typing Mathematical Notation

These exercises use MathQuill, a web formula editor designed to make typing Maths easy and beautiful. Watch the animation below to see how common mathematical notation can be created using your keyboard.

MathQuill Animation

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