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

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General Binomial Expansion
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What is the fully expanded form of (2+x)6(2 + x)^6?

64+192x+240x2+160x3+60x4+12x5+x664 + 192x + 240x^2 + 160x^3 + 60x^4 + 12x^5 + x^6

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

x<1|x| < 1

What is the expansion of (1+2x)1(1 + 2x)^{-1} up to and including the x3x^3 term?

12x+4x28x3+1 - 2x + 4x^2 - 8x^3 + \ldots

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

5913659136

What is the probability of winning a lottery by choosing 6 numbers correctly out of 49?

113,983,816\frac{1}{13,983,816}

What is (3+2x)4(3 + 2x)^4 when fully expanded?

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

Using (1+2x)61+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 expansion of (x+1x)4(x + \frac{1}{x})^4?

x4+4x2+6+4x2+1x4x^4 + 4x^2 + 6 + \frac{4}{x^2} + \frac{1}{x^4}

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

240240

What is the expansion of (112x)12(1 - \frac{1}{2}x)^{\frac{1}{2}} up to x3x^3?

114x132x21128x3+1 - \frac{1}{4}x - \frac{1}{32}x^2 - \frac{1}{128}x^3 + \ldots

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