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Question

Mathematics Question on Binomial Theorem for Positive Integral Indices

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

Answer

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

(2x−3)6(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

= 64x6−6(32x5)(3)+15(16x4)(9)−20(8x3)(27)+15(4x2)(81)−6(2x)(243)+72964 x^6 - 6(32x^5)(3) + 15(16 x^4)(9) - 20(8x^3)(27) +15(4 x^2)(81) - 6(2x)(243) + 729

= 64x6−576x5+2160x4−4320x3+4860x2−2916x+72964x^6 - 576 x^5 + 2160x^4 - 4320 x^3 + 4860 x^2 - 2916x +729