Use the binomial theorem to ﬁnd the coeﬃcient of xayb in the expansion of (5x2 + 2y3)6, where a) a = 6, b = 9. b) a = 2, b = 15.

Question

2 months ago

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c) a = 3, b = 12. d) a = 12, b = 0. e) a = 8, b = 9.

1 answer:

zzz [12.3K] · Answer 1 · 2026-03-22T14:12:09+03:00

Answer:

Step-by-step explanation:

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 20 15 6 1

We employ these for the expansion of (5x² + 2y³)⁶

1(5x²)⁶(2y³)⁰ + 6(5x²)⁵(2y³)¹ + 15(5x²)⁴(2y³)² + 20(5x²)³(2y³)³+ 15(5x²)²(2y³)⁴+ 6(5x²)¹(2y³)⁵ + 1(5x²)⁰(2y³)⁶

78125ₓ¹²+187500ₓ¹⁰ y³ +37500ₓ⁸y⁶+20000ₓ⁶y⁹+6000x⁴y¹²+960x²y¹⁵+2y¹⁸

a.)a = 6, b = 9. the coefficient of xᵃyᵇ ( 20000ₓ⁶y⁹) = 20000

b) a = 2, b = 15. the coefficient of xᵃyᵇ ( 960x²y¹⁵) = 960

c) a = 3, b = 12. the coefficient of xᵃyᵇ is not present

d) a = 12, b = 0 the coefficient of xᵃyᵇ ( 78125ₓ¹²) = 78125

e) a = 8, b = 9. the coefficient of xᵃyᵇ is not present