Question

The number of terms in the expansion of (1-2x+x2)30 is

Answer 1

no. of terms will be 31

Answer 2

Let me rewrite the given, so that,

$(1-2x+x^2)^{30} \\ \\ ((1-x)^2)^{30} \\ \\ (1-x)^{2 \times 30} \\ \\ (1-x)^{60} \\ \\ \\ OR \\ \\ \\ (1-2x+x^2)^{30} \\ \\ (x^2-2x+1)^{30} \\ \\ ((x-1)^2)^{30} \\ \\ (x-1)^{2 \times 30} \\ \\ (x-1)^{60}$

Whichever we take either (x - 1)⁶⁰ or (1 - x)⁶⁰, the no. of terms in the decimal expansion is 60 + 1 = 61.

So 61 is the answer.

Plz ask me if you have any doubt on my answer.

Thank you...