Find the coefficient of the given term in the binomial expansion.

Question

Find the coefficient of the given term in the binomial expansion.

Answer 1

One of the properties of the Binomial Theorem is that the "r + 1"th term of (x + y)ⁿ can be written as:

T_r+1 = _nC_r• x^n-ry^r

In your case n = 10 and you want the "x^n-r" term to be x6 so r = 4

T₄₊₁ = ₁₀C₄•x^10-4y⁴

T₅ = 210x⁶y⁴ but, in your case, although x = x, y is equal to -5 so you need to plug that in:

T₅ = 210x⁶(-5)⁴ now, do the power and the multiplication to get the term