Given, (1 – x)2 (2 + x)5
= (1 + x2 - 2) (1 + 5C1 25– 1 x1 + 5C2 2 5–2 x2 + 5C3 2 5–3 x3 + 5C4 25 – 4 x4 +5C5 25 – 5 x5)
= (1 + x2 - 2x) (1 + 5. 24 .x + 10. 23 x2 + 10 . 22 x3 + 5 . 2 . x4 + x5 )
= (1 + x2 – 2x) (1 + 80x + 80x2 + 40x3 + 10x4 + x 5 )
∴ Coefficient of x4 = 80 – 80 + 10 = 10