The Binomial Theorem

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What is the Binomial Theorem?

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The Binomial Theorem provides a formula for expanding expressions of the form (a + b)^n, where n is a non-negative integer. It states that (a + b)^n = Σ (n choose k) * a^(n-k) * b^k for k = 0 to n.

Tags

CCSS.HSA.APR.C.5

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What is Pascal's Triangle?

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Pascal's Triangle is a triangular array of the binomial coefficients. Each number is the sum of the two directly above it. It is used to find coefficients in the expansion of (a + b)^n.

Tags

CCSS.HSA.APR.C.5

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What is a Monomial?

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A monomial is a polynomial with only one term, such as 3x^2 or -5.

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What is a Binomial?

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A binomial is a polynomial with two terms, such as (x + 2) or (3x^2 - 1).

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What is a Trinomial?

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A trinomial is a polynomial with three terms, such as (x^2 + 3x + 2).

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What is a Polynomial?

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A polynomial is an expression consisting of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents.

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How do you expand (a + b)^n using the Binomial Theorem?

Back

To expand (a + b)^n, use the formula: (a + b)^n = Σ (n choose k) * a^(n-k) * b^k for k = 0 to n.

Tags

CCSS.HSA.APR.C.5

Front

What is the formula for (n choose k)?

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The formula for (n choose k) is n! / (k!(n-k)!), where n! is the factorial of n.

Tags

CCSS.HSA.APR.C.5

Front

What is the 7th row of Pascal's Triangle?

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The 7th row of Pascal's Triangle is 1, 7, 21, 35, 35, 21, 7, 1.

Tags

CCSS.HSA.APR.C.5

Front

Expand (2x + 5)^4 using the Binomial Theorem.

Back

(2x + 5)^4 = 16x^4 + 160x^3 + 600x^2 + 1000x + 625.

Tags

CCSS.HSA.APR.C.5