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koefisien dgn kombinasi

(2a + b/2)⁶ =

= 6c0 (2a)⁶  +6c1 (2a)⁵(b/2) + 6c2 (2a)⁴(b/2)² + 6c3 (2a)³(b/2)³ + 6c4 (2a)²(b/2)⁴ + 6c5 (2a)(b/2)⁵ + 6c6 (b/2)⁶


= 64 a⁶ + 6(32)(a⁵)(1/2)(b) + 15 (16)(a⁴)(1/4)(b²) + 20  (8)(a³)(1/8)(b³) + 15 (4)(a²)(1/16)(b⁴) + 6 (2)(a)(1/32)(b⁵) + 1 (1/64)(b⁶)
.
= 64 a⁶ + 96 a⁵b + 60 a⁴b² + 20 a³b³ + 15/4 a²b⁴ + 3/8 ab⁵ + 1/64 b⁶
..

Kelas : XI
Kategori : Binomial Newton

[c] (2a + ᵇ/₂)⁶

= ₆C₀.(2a)⁶ + ₆C₁.(2a)⁵(ᵇ/₂)¹ + ₆C₂.(2a)⁴(ᵇ/₂)² + ₆C₃.(2a)³(ᵇ/₂)³ + ₆C₄.(2a)²(ᵇ/₂)⁴ + ₆C₅.(2a)¹(ᵇ/₂)⁵ + ₆C₆.(ᵇ/₂)⁶

= 64a⁶ + 6(32a⁵)(ᵇ/₂) + 15(16a⁴)(b²/4) + 20(8a³)(b³/8) + 15(4a²)(b⁴/16) + 6(2a)(b⁵/32) + (b/64)

= 64a⁶ + 96a⁵b + 60a⁴b² + 20a³b³ + ¹⁵/₄.a²b⁴ + ³/₈.ab⁵ + ᵇ/₆₄

[d] (2a/3 + 1/3b)⁸

= ₈C₀.(2a/3)⁸ + ₈C₁.(2a/3)⁷(1/3b)¹ + ₈C₂.(2a/3)⁶(1/3b)² + ₈C₃.(2a/3)⁵(1/3b)³ + ₈C₄.(2a/3)⁴(1/3b)⁴ + ₈C₅.(2a/3)³(1/3b)⁵ + ₈C₆.(2a/3)²(1/3b)⁶ + ₈C₇.(2a/3)¹(1/3b)⁷ + ₈C₈.(1/3b)⁸

= 256a⁸/6561 + 8(128a⁷/2187)(1/3b) + 28(64a⁶/729)(1/9b²) + 56(32a⁵/243)(1/27b³) + 70(16a⁴/81)(1/81b⁴) + 56(8a³/27)(1/243b⁵) + 28(4a²/9)(1/729b⁶) + 8(2a/3)(1/2187b⁷) + (1/6561b⁸)

= 256a⁸/6561 + 1024a⁷/6561b + 1792a⁶/6561b² + 1792a⁵/6561b³ + 1120a⁴/6561b⁴ + 448a³/6561b⁵ + 112a²/6561b⁶ + 16a/6561b⁷ + 1/6561b⁸