General Binomial Expansion (Edexcel A-Level Mathematics): Quizzes

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General Binomial Expansion
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What is the formula for the binomial coefficient (nr)\binom{n}{r}?

n!r!(n−r)!\frac{n!}{r!(n-r)!}

For (1+x)n(1 + x)^n where n∈Rn \in \mathbb{R}, what condition must xx satisfy?

∣x∣<1|x| < 1

What is the constant term in the expansion of (2+x)6(2 + x)^6?

6464

What is the coefficient of xx in the expansion of (1+2x)−1(1 + 2x)^{-1} up to x3x^3?

−2-2

What is the full expansion of (3+2x)4(3 + 2x)^4?

81+216x+216x2+96x3+16x481 + 216x + 216x^2 + 96x^3 + 16x^4

What is the coefficient of the x6x^6 term in (2+x)12(2 + x)^{12}?

5913659136

Using (1+2x)6≈1+12x+60x2(1 + 2x)^6 \approx 1 + 12x + 60x^2, what is the approximation for 1.0461.04^6?

1.2641.264

What is the coefficient of x2x^2 in (1−13x)4(1 - \frac{1}{3}x)^4?

23\frac{2}{3}

What is the coefficient of x8x^8 in (1+2x2)6(1 + 2x^2)^6?

240240

What is the constant term in the expansion of (x+1x)4(x + \frac{1}{x})^4?

66

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