Binomial Theorem

Examples, videos, solutions, and lessons to help High School students know and apply the Binomial Theorem for the expansion of (x + y)ⁿ in powers ofx and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle.

Suggested Learning Targets

• For small values of n, use Pascal’s Triangle to determine the coefficients of the binomial expansion.
• Use the Binomial Theorem to find the nth term in the expansion of a binomial to a positive power.

Common Core: HSA-APR.C.5

Using Pascal’s Triangle

Binomial Expansion Using Pascal’s Triangle
This video explains binomial expansion using Pascal’s triangle.
(x + 3)⁴

Ex 1: The Binomial Theorem Using Pascal’s Triangle
This provides a basic example of how to expand a binomial raised to a power using the binomial theorem. The combinations are evaluated using Pascal’s Triangle.
(x - 4)⁵

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Ex 2: The Binomial Theorem Using Pascal’s Triangle
This provides a basic example of how to expand a binomial raised to a power using the binomial theorem. The combinations are evaluated using Pascal’s Triangle.
(5x - 2)⁴

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Ex 3: The Binomial Theorem Using Pascal’s Triangle
This provides a basic example of how to expand a binomial raised to a power using the binomial theorem. The combinations are evaluated using Pascal’s Triangle.
(2x - 3y²)⁴

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Using Combinations

The Binomial Theorem using Combination
This video shows how to apply the binomial theorem.
(x + 3)⁴

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Ex 1: The Binomial Theorem Using Combinations
This provides a basic example of how to expand a binomial raised to a power using the binomial theorem.
(x + 2)⁵

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Ex 2: The Binomial Theorem Using Combinations
This provides a basic example of how to expand a binomial raised to a power using the binomial theorem.
(2x - 3)⁴

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Ex 3: The Binomial Theorem Using Combinations
This provides a basic example of how to expand a binomial raised to a power using the binomial theorem.
(3x² - 5y)⁴

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