Biết rằng (3x – 1)^7 = a0 + a1x + a2x2 + a3x3 + a4x4 + a5x5 + a6x6 + a7x7. Hãy tính: a) a0 + a1 + a2 + a3 + a4 + a5 + a6 + a7; b) a0 + a2 + a4 + a6.

Hướng dẫn giải

Có (3x – 1)⁷

=C70(3x)7+C71(3x)6(−1)+C72(3x)5(−1)2+C73(3x)4(−1)3

+C74(3x)3(−1)4+C75(3x)2(−1)5+C76(3x)1(−1)6+C77(−1)7

= 2187x7 – 5103x6 + 5103x5 – 2835x4 + 945x3 – 189x2 + 21x – 1.

a) a₀ + a₁ + a₂ + a₃ + a₄ + a₅ + a₆ + a₇

= (–1) + 21 + (–189) + 945 + (–2835) + 5103 + (–5103) + 2187 = 128.

b) a₀ + a₂ + a₄ + a₆

= (–1) + (–189) + (–2835) + (–5103) = –8128.