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AssignmentMultiple Choice

The Binomial Theorem

Question 1 • Adv. Algebra II S1 Original

Use the binomial theorem to expand (a + b)6.

Answer
A
6C0a6 + 6C1a5b + 6C2a4b2 + 6C3a3b3 + 6C4a2b4 + 6C5ab5
B
6C0a6b + 6C1a5b2 + 6C2a4b3 + 6C3a3b4 + 6C4a2b5 + 6C5ab6 + 6C6b7
C
6C0a6 + 6C1a5b + 6C2a4b2 + 6C3a3b3 + 6C4a2b4 + 6C5ab5 + 6C6b6

Explanation

By the binomial theorem, (a + b)^6 = Σₖ₌₀⁶ ⁶Cₖ a⁶⁻ᵏbᵏ. The terms run from ⁶C₀a⁶ through ⁶C₆b⁶, so the expansion includes seven terms, with the final term b⁶. Choice C gives all of these terms; choice A leaves off the final term.

AI-written and checked against the verified answer.

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