Question

Question 3 Expand the expression (2x – 3)^6

Class X1 - Maths -Binomial Theorem Page 166

Answer 1

$(2x-3)^6\\use\:the\:formula,\\(x-y)^n= ^nC_0x^n- ^nC_1x^{n-1}.y+ ^nC_2x^{n-2}y^2-.....+(-1)^n ^nC_ny^n$

(2x - 3)⁶ = ⁶C₀(2x)⁶ - ⁶C₁(2x)⁵(3) + ⁶C₂(2x)⁴(3)² - ⁶C₃(2x)³(3)³+ ⁶C₄(2x)²(3)⁴ - ⁶C₅(2x)(3)⁵ + ⁶C₆(3)⁶

= ⁶C₀ 64x⁶ - ⁶C₁ 32x⁵ × 3 + ⁶C₂ 16x⁴ × 9 - ⁶C₃ 8x³ × 27 + ⁶C₄ 4x² × 81 - ⁶C₅ 2x × 243 + ⁶C₆ 729

= 64x⁶ - 6 × 32 × 3 × x⁵ + {6 × 5}/2 16x⁴ × 9 - {6 × 5 × 4 × 8x³ × 27}/6 + {6 × 5}/2 × 4x² × 81 - 6 × 2x × 243 + 729

= 64x⁶ - 576x⁵ + 2160x⁴ -4320x³ + 4860x² -2916x + 729

Answer 2

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