Using binomial theorem, expand each of the following: (2x – 3) 6

Question

Philoid · Accepted Answer

To find: Expansion of (2x – 3)⁶

Formula used: (i)

(ii) (a+b)ⁿ = ⁿC₀aⁿ + ⁿC₁a^n-1b + ⁿC₂a^n-2b² + …… +ⁿC_n-1ab^n-1 + ⁿC_nbⁿ

We have, (2x – 3)⁶

⇒ [⁶C₀(2x)⁶]+[⁶C₁(2x)^6-1(-3)¹]+[⁶C₂(2x)^6-2(-3)²]+[⁶C₃(2x)^6-3(-3)³]+ [⁶C₄(2x)^6-4(-3)⁴] + [⁶C₅(2x)^6-5(-3)⁵] + [⁶C₆(-3)⁶]

⇒ [(1) (64x⁶)] – [(6)(32x⁵)(3)] + [15(16x⁴)(9)] – [20(8x³)(27)] + [15(4x²)(81)] – [(6)(2x)(243)] + [(1)(729)]

⇒ 64x⁶ – 576x⁵ + 2160x⁴ – 4320x³ + 4860x² – 2916x + 729

Ans) 64x⁶ – 576x⁵ + 2160x⁴ – 4320x³ + 4860x² – 2916x + 729