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Binomial Theorem (Discrete)

Expansion of (x+y)ⁿ.

Key idea

Expansion of (x+y)ⁿ.

In depth

(x + y)ⁿ = Σ C(n, k)xⁿ⁻ᵏyᵏ: choosing k of the n factors to give y counts the coefficient. Setting x = y = 1 gives 2ⁿ, showing the number of subsets.

Worked example

(x + y)⁴ = x⁴ + 4x³y + 6x²y² + 4xy³ + y⁴.

Formula

Σ C(n,k)xᵏyⁿ⁻ᵏ

Real-world uses

Common mistake

Forgetting coefficients when one term has a number like 2y.

How to learn this

  1. Read the key idea and say it in your own words.
  2. Work through the worked example, then try a similar problem.
  3. Use the interactive lesson’s visual and mini-quiz to check the pattern.

Frequently asked questions

What is Binomial Theorem (Discrete)?

Expansion of (x+y)ⁿ. It is a topic at the advanced level in Discrete Math & Number Theory.

What is the formula for Binomial Theorem (Discrete)?

The key formula is Σ C(n,k)xᵏyⁿ⁻ᵏ.

Where is Binomial Theorem (Discrete) used in real life?

Real-world examples: Expanding (x + y)ⁿ quickly in exams and calculating combinations in probability.

What should I learn before Binomial Theorem (Discrete)?

Make sure you are comfortable with Binomial Coefficients, the previous topic in Discrete Math & Number Theory.

What is a common mistake with Binomial Theorem (Discrete)?

Forgetting coefficients when one term has a number like 2y.

How can I practise Binomial Theorem (Discrete)?

Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.

What comes after Binomial Theorem (Discrete)?

Move on to Multinomial Coefficients next.

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