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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River Crossing

Three interactive versions of the traditional river crossing puzzles. The objective is to get all of the characters to the other side of the river without breaking any of the rules.

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Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

Maths Map

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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.

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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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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.

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