# Binomial Theorem

## Exercises in expanding powers of binomial expressions and finding specific coefficients.

##### BracketsPascal's TriangleLevel 1Level 2Exam-StyleDescriptionHelpMore 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 $$a$$ 2. Expand $$(x+2)^4$$ in descending powers of $$x$$ 3. Expand $$(2x+3y)^5$$ in descending powers of $$x$$ 4. Expand $$(c-d)^6$$ in descending powers of $$c$$ 5. Expand $$(x-3)^4$$ in descending powers of $$x$$ 6. Expand $$(2w-3)^5$$ in descending powers of $$w$$ 7. Give the first 3 terms of the expansion of $$(2j+5k)^7$$ in descending powers of $$j$$ 8. Give the last 3 terms of the expansion of $$(3e-2f)^6$$ in descending powers of $$e$$ 9. Expand $$(3x+ \frac{y}{2})^3$$ in descending powers of $$x$$ 10. Expand $$(4x-\frac{1}{2x})^5$$ in descending powers of $$x$$
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This is Binomial Theorem level 1. You can also try:
Level 2

## Instructions

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## Go Maths

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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.

## Using a Scientific Calculator

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

## 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.

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