Expand Using the Binomial Theorem (x-y)^2

Problem

(x−y)2

Solution

1. Identify the terms and the exponent for the Binomial Theorem formula (a+b)n=(∑_k=0^n)((n/k))*a(n−k)*bk) Here, a=x b=−y and n=2

2. Apply the formula by writing out the summation for k=0,1,2

(2/0)x2*(−y)0+(2/1)x1*(−y)1+(2/2)x0*(−y)2)))

3. Calculate the binomial coefficients using the formula (n/k)=(n!)/(k!(n−k)!))

(2/0)=1)

(2/1)=2)

(2/2)=1)

4. Substitute the coefficients and simplify the powers of −y

1⋅x2⋅1+2⋅x⋅(−y)+1⋅1⋅y2

5. Simplify the signs and combine the terms.

x2−2*x*y+y2

Final Answer

(x−y)2=x2−2*x*y+y2

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