Prove that a b7 in (a-2b)12

Let a5b7 occurs in the (r + 1)th term, in the expansion of (a - 2b)12 given by I2Cr. a12 – r(-2b)r. Then 12 – r = 5. This gives r= 7. Thus the coefficient of a5b7 is 12C5 (-2)7 = (-128) = (792) (-128) = -101376

Q16 of 25 Page 8

Prove that a b⁷ in (a-2b)¹²

Let a⁵b⁷ occurs in the (r + 1)th term, in the expansion of (a - 2b)¹² given by ^I2C_r. a^{12 – r}(-2b)^r. Then 12 – r = 5. This gives r= 7.
Thus the coefficient of a⁵b⁷ is

¹²C₅ (-2)⁷ =

(-128) = (792) (-128) = -101376