Expand (3 - 2x)⁶. What is the coefficient of the sixth term?

Solution:

Given (3 - 2x)⁶

Using binomial theorem, (x + a)ⁿ = 1 + nx + [n(n - 1)/2!]x² + [n(n - 1)(n - 2)/3!]x³ +....

Here n = 6

(3 - 2x)⁶ = 3⁶ + 6 × 3⁵(-2x) + 15 × 3⁴(-2x)² + 20.3³(-2x)³ + 15 × 3²(-2x)⁴ + 6 × 3(-2x)⁵ + (-2x)⁶

(3 - 2x)⁶ = 729 + 1458(-2x) + 1215(4x²) - 540(8x³) + 135(16x⁴) - 18(32x⁵) + 64x⁶

(3 - 2x)⁶ = 729 - 2916x + 4860x² - 4320x³ + 2160x⁴ - 576x⁵ + 64x⁶

Coefficient of 6th term is -576

Expand (3 - 2x)⁶. What is the coefficient of the sixth term?

Summary:

By Expanding (3 - 2x)⁶, the coefficient of the sixth term is -576.