Expand Using the Binomial Theorem (x+y)^5

Problem

(x+y)5

Solution

1. Identify the parameters of the binomial (a+b)n where a=x b=y and n=5

2. Apply the Binomial Theorem formula, which states (a+b)n=(∑_k=0^n)((n/k))*a(n−k)*bk)

3. Write out the terms for k=0 to k=5

(5/0)x5*y0+(5/1)x4*y1+(5/2)x3*y2+(5/3)x2*y3+(5/4)x1*y4+(5/5)x0*y5))))))

4. Calculate the binomial coefficients using Pascal's Triangle or the formula (n/k)=(n!)/(k!(n−k)!)) which results in 1, 5, 10, 10, 5, 1$.

5. Simplify each term by multiplying the coefficients with the variables.

Final Answer

(x+y)5=x5+5*x4*y+10*x3*y2+10*x2*y3+5*x*y4+y5

Want more problems? Check here!