Binomial Theorem Flashcardizz

Front

What is the Binomial Theorem?

Back

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.

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Back

Front

What is the Binomial expansion of (x + 1)^5?

Back

x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1.

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What is row 7 of Pascal's Triangle?

Back

1, 7, 21, 35, 35, 21, 7, 1.

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Front

What is the general term in the expansion of (a + b)^n?

Back

The general term is given by T(k+1) = (n choose k) * a^(n-k) * b^k.

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What does (n choose k) represent?

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(n choose k) or C(n, k) represents the number of ways to choose k elements from a set of n elements without regard to the order of selection.

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What is the value of (1 + x)^n when n = 0?

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(1 + x)^0 = 1.

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What is the value of (1 + x)^1?

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(1 + x)^1 = 1 + x.

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What is the coefficient of x^3 in the expansion of (2x + 3)^5?

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The coefficient of x^3 is 10 * (2^3) * (3^2) = 10 * 8 * 9 = 720.