Binomial Theorem Math Example 3

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Example 3

easy
Expand (a+b)4(a + b)^4 using Pascal's triangle.

Solution

  1. 1
    Row 4 of Pascal's triangle: 1, 4, 6, 4, 1.
  2. 2
    (a+b)4=a4+4a3b+6a2b2+4ab3+b4(a+b)^4 = a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4.

Answer

a4+4a3b+6a2b2+4ab3+b4a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4
Pascal's triangle gives the binomial coefficients directly. Row nn has n+1n+1 entries that serve as the coefficients in the expansion of (a+b)n(a+b)^n.

About Binomial Theorem

The binomial theorem gives the expansion of (a + b)^n as a sum of terms involving binomial coefficients: (a+b)^n = sum of C(n,k) * a^(n-k) * b^k. Each coefficient (nk)\binom{n}{k} counts the number of ways to choose kk copies of bb from nn factors.

Learn more about Binomial Theorem →

More Binomial Theorem Examples

Example 1 medium

Expand [formula] using the Binomial Theorem.

Example 2 hard

Find the coefficient of [formula] in the expansion of [formula].

Example 4 medium

What is [formula]?

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