What is the coefficient of the term x⁷y in the expansion of (x + y)⁸?

Solution:

We have to find the coefficient of x⁷y in the expansion of (x + y)⁸

Expanding using the binomial expansion formula

(x + y)⁸ = ⁸C₀ x⁸ y⁰ + ⁸C₁ x^{8 - 1} y¹ + ⁸C₂ x^{8 - 2} y² + ⁸C₃ x^{8 - 3} y³ + ⁸C₄ x^{8 - 4} y⁴ + ⁸C₅ x^{8 - 5} y⁵ + ⁸C₆ x^{8 - 6} y⁶ + ⁸C₇ x^{8 - 7} y⁷ + ⁸C₈ x^{8 - 8} y⁸

By further calculation

(x + y)⁸ = ⁸C₀ x⁸ y⁰ + ⁸C₁ x7 y¹ + ⁸C₂ x⁶ y² + ⁸C₃ x⁵ y³ + ⁸C₄ x⁴ y⁴ + ⁸C₅ x³ y⁵ + ⁸C₆ x² y⁶ + ⁸C₇ x¹ y⁷ + ⁸C₈ x⁰ y⁸

Therefore, the coefficient of the term x⁷y is 8.

What is the coefficient of the term x⁷y in the expansion of (x + y)⁸?

Summary:

The coefficient of the term x⁷y in the expansion of (x + y)⁸ is 8.