We have (1 + 2x) 6 (1 – ) 7
= [1 + 6C1 (2x) + 6C2 (2x)2 + 6C3 (2x)3 + 6C4 (2x)4 + 6C5 (2x) 5 + 6C6 (2x) 6 ] × [1 – 7C1 x + 7C2 x 2 – 7C3x3 + 7C4 x 4 – 7C5 x5 + 7C6 x6 –7C7 x7 ] ÷ (1 + 12x + 60x2 + 160x3 + 240x 4 + 192x5 + 64x6 ) × (1 – 7 x + 21x2 – 35x3 + 35x4 – 21x5 +x6 –x7 )
∴ Coefficients of 5 in the product
= 1 × (– 21) + 12 × 35 + 60 × (– 35) + 160 × 21 + 240 × (– 7) + 192 × 1
= – 21 + 420 – 2100 + 3360 – 1680 + 192
= 171