Find the co-efficient of x2 in (3 − x)10

To find the coefficient of x² in (3 - x)¹⁰, we can use the binomial theorem, which states that:

(a - b)ⁿ = Σ (from k=0 to n) [nCk * a^(n-k) * (-b)^k]

where nCk denotes "n choose k", or the number of ways to choose k items from a set of n.

In this case, a = 3, b = x, and n = 10. We want to find the coefficient of x², so we set k = 2.

Substituting these values into the binomial theorem gives:

10C2 * 3^(10-2) * (-x)^2

= 45 * 3^8 * x²

= 45 * 6561 * x²

= 295245 * x²

So, the coefficient of x² in (3 - x)¹⁰ is 295245.