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12.6 The Binomial Theorem

Focus on binomial coefficient and expand a binomial square.

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01Binomial coefficientsWorked steps · five questions 02Expanding with the Binomial TheoremWorked steps · five questions 03Finding a specific termWorked steps · five questions

Lesson brief and rules

12.6 The Binomial Theorem

The coefficient of $x^{n-1}y$ in $(x+y)^{n}$ is $n$ .

Worked example

1

01 / Find the coefficient of

x^{3}y

(x+y)^{4}

02 / Choose which one of the

4

factors contributes

y

; coefficient is

4

03 / Answer:

4

Worked example 2 · Expand a binomial square

Expand $(x+4)^{2}$ .

Use $(x+a)^{2}=x^{2}+2ax+a^{2}$ . Answer: $x^{2}+8x+16$

15 questions covering every idea, with a worked answer for each.Start practice ↗

Textbook reference: Stewart, Redlin & Watson, Precalculus: Mathematics for Calculus, 7th ed. (Cengage, 2016). The explanations and practice here are original, organized by textbook section.

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12.6 The Binomial Theorem

Ideas in this lesson

12.6 The Binomial Theorem