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The coefficient of x4 in the expansion of 1 x x2 x36 in powe: (Mathematics) | DivineJEE

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Mathematics

Exam

Mathematics

The coefficient of x⁴ in the expansion of
(1 + x + x² + x³)⁶ in powers of x, is ______.

Explanation

(1 + x + x² + x³)⁶

= ((1 + x) (1 + x²))⁶

= (1 + x)⁶(1 + x²)⁶ $\\= \sum\limits_{r = 0}^6 {{}^6{C_r}.{x^r}} \\$ $\sum\limits_{r = 0}^6 {{}^6{C_r}.{x^{2r}}}$

Coefficient of x⁴ = ⁶C₀ ⁶C₂ + ⁶C₂ ⁶C₁ + ⁶C₄ ⁶C₀ = 120

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