# AlGeo 3 The Binomial Theorem

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 What is the coefficient of the x5y5-term in the binomial expansion of (2x – 3y)10? 10C5(2)5(3)5 10C5(2)5(-3)5 -10C5(2)5(-3)5 10C5(2)5(3) B) 10C5(2)5(-3)5 Which expression represents the fourth term in the binomial expansion of (e + 2f)10? 10C3(e7)(2f)3 10C3(e7)(f)3 10C4(e6)(2f)4 10C4(e6)(f)4 A) 10C3(e7)(2f)3 How many terms are in the binomial expansion of (3x + 5)9? 8 9 10 11 C)10 What is the coefficient of the third term in the binomial expansion of (a + b)6? 1 15 20 90 B) 15 Which statement about the simplified binomial expansion of (a + b)n, where n is a positive integer, is true? The value of the binomial coefficient nC0 is n – 1 for all values of n. The values of nC1 and nCn-1 are equal to 1. The values of nC0 and nCn are equal to 1. The value of the binomial coefficient nC1 is n – 1 for all values of n. C) The values of nC0 and nCn are equal to 1. What are the coefficients for the binomial expansion of (p + q)6? 1, 8, 28, 56, 70, 56, 28, 8, 1 1, 6, 15, 20, 15, 6, 1 1, 5, 10, 10, 5, 1 1, 4, 6, 4, 1 B) 1, 6, 15, 20, 15, 6, 1 The following list gives the coefficients for the binomial expansion of (x + y)10. What is the value of B? 1, 10, 45, 120, 210, 252, 210, B, 45, 10, 1 1 10 45 120 Not, B) 10 What is the binomial expansion of (x + 2)4? x4 + 4×3 + 6×2 + 4x + 1 8×3 + 24×2 + 32x x4 + 8×3 + 24×2 + 32x + 16 2×4 + 8×3 + 12×2 + 8x + 2 C) x4 + 8×3 + 24×2 + 32x + 16 What is the coefficient of the last term in the binomial expansion of (x + 1)9? 0 1 9 10 B) 1 How many terms are in the binomial expansion of (2x + 3)5? 4 5 6 7 Not, A) 4 The side length, s, of a cube is 4×2 + 3. If V = s3, what is the volume of the cube? 64×6 + 144×4 + 108×2 + 27 64×6 + 48×4 + 12×2 + 1 4×6 + 36×4 + 108×2 + 27 4×6 + 12×4 +12×2 + 1 A) 64×6 + 144×4 + 108×2 + 27 What is the coefficient of the x9y-term in the binomial expansion of (2y + 4×3)4? 4 32 128 512 D) 512 What is the binomial expansion of (2x – 3)5? (2x)5 – 15(2x)4 + 90(2x)3 – 270(2x)2 + 405(2x) – 243 (2x)5 + 15(2x)4 – 90(2x)3 + 270(2x)2 – 405(2x) + 243 (2x)5 + 15(2x)4 + 90(2x)3 + 270(2x)2 + 405(2x) + 243 2(x)5 – 30(x)4 + 180(x)3 – 540(2x)2 + 810(x) – 243 Not, B) (2x)5 + 15(2x)4 – 90(2x)3 + 270(2x)2 – 405(2x) + 243

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