Binomial Expansion Worksheet

Grade 10 Math worksheet covering binomial expansion using Pascal's Triangle and the binomial theorem.

Grade 10 Math AlgebraBinomial Expansion

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TextFill in the BlanksShort AnswerMultiple ChoiceLong Answer

Standards

CCSS.MATH.CONTENT.HS.A.APR.C.5

Topics

MathAlgebraBinomial ExpansionPascal's TriangleBinomial Theorem

7 sections · Free to use · Printable

Binomial Expansion

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Read each question carefully and show all your work. Use Pascal's Triangle or the Binomial Theorem to expand the given expressions.

Pascal's Triangle is a triangular array of the binomial coefficients. Each number is the sum of the two numbers directly above it.

Fill in the missing numbers in Pascal's Triangle below:

Row 0: 1

Row 1: 1 1

Row 2: 1 2 1

Row 3: 1 3 3 1

Row 4: 1 _ _ _ 1

Row 5: 1 _ _ _ _ 1

1. The coefficients in the expansion of (a + b)ⁿ are given by the triangle.

2. The binomial theorem provides a formula for expanding any power of a .

3. The sum of the exponents of a and b in each term of a binomial expansion is always equal to .

1. Expand (x + y)³ using Pascal's Triangle.

2. Expand (2a - b)⁴ using the binomial theorem.

1. What is the coefficient of the x²y³ term in the expansion of (x + y)⁵?

1. Find the 3rd term in the expansion of (3x - 2y)⁶.