Question

Expand the expression \((2x - 3) ^6\).

Answer 1

By using Binomial Theorem, the expression \((2x - 3) ^6\) can be expanded as

 \((2x - 3) ^6 \) = \( ^6C_0(2x)^6 - ^6C_1(2x)^5(3) + ^6C_2(2x)^4(3)^2 - ^6C_3(2x)^3(3)^3 + ^6C_4(2x)^2(3)^4 - \)\(^6C_5(2x)(3)^5 + ^6C_6(3)^6\)

= \(64 x^6 - 6(32x^5)(3) + 15(16 x^4)(9) - 20(8x^3)(27) +15(4 x^2)(81) - 6(2x)(243) + 729\)

= \(64x^6 - 576 x^5 + 2160x^4 - 4320 x^3 + 4860 x^2 - 2916x +729\)