Expand Using the Binomial Theorem (x-5)^3

Problem

(x−5)3

Solution

1. Identify the parameters for the Binomial Theorem formula (a+b)n=(∑_k=0^n)((n/k))*a(n−k)*bk) where a=x b=−5 and n=3

2. Write the expansion using the binomial coefficients for n=3 which are 1, 3, 3, 1$.

(x−5)3=(3/0)x3*(−5)0+(3/1)x2*(−5)1+(3/2)x1*(−5)2+(3/3)x0*(−5)3))))

3. Evaluate the binomial coefficients and the powers of −5

(x−5)3=1⋅x3⋅1+3⋅x2⋅(−5)+3⋅x⋅25+1⋅1⋅(−125)

4. Simplify each term by performing the multiplication.

(x−5)3=x3−15*x2+75*x−125

Final Answer

(x−5)3=x3−15*x2+75*x−125

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