Expand Using the Binomial Theorem (a-b)^2

Problem

(a−b)2

Solution

1. Identify the terms and the exponent for the Binomial Theorem formula (x+y)n=(∑_k=0^n)((n/k))*x(n−k)*yk)

2. Substitute x=a y=−b and n=2 into the expansion.

3. Write the summation terms for k=0 k=1 and k=2

(2/0)a2*(−b)0+(2/1)a1*(−b)1+(2/2)a0*(−b)2)))

4. Calculate the binomial coefficients (2/0)=1) (2/1)=2) and (2/2)=1)

1⋅a2⋅1+2⋅a⋅(−b)+1⋅1⋅b2

5. Simplify the signs and terms to reach the final polynomial.

a2−2*a*b+b2

Final Answer

(a−b)2=a2−2*a*b+b2

Want more problems? Check here!