9
QuizMultiple Choice

The Binomial Theorem

Question 9 • Adv. Algebra II S1 Original

What is the binomial expansion of (x + 2)4?

Answer
A
x4 + 4x3 + 6x2 + 4x + 1
B
8x3 + 24x2 + 32x
C
x4 + 8x3 + 24x2 + 32x + 16
D
2x4 + 8x3 + 12x2 + 8x + 2

Explanation

Use the binomial coefficients 1, 4, 6, 4, 1 and multiply by the corresponding powers of 2: (x + 2)⁴ = x⁴ + 4x³(2) + 6x²(2²) + 4x(2³) + 2⁴. Simplifying gives x⁴ + 8x³ + 24x² + 32x + 16, which is choice C.

AI-written and checked against the verified answer.

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