Expand Using the Binomial Theorem (2x-3)^3

Problem

(2*x−3)3

Solution

1. Identify the terms and the exponent for the binomial expansion (a+b)n where a=2*x b=−3 and n=3

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

3. Write out the individual terms of the expansion using the combinations (3/0)) (3/1)) (3/2)) and (3/3))

(3/0)(2*x)3*(−3)0+(3/1)(2*x)2*(−3)1+(3/2)(2*x)1*(−3)2+(3/3)(2*x)0*(−3)3))))

4. Evaluate the combinations and the powers for each term.

1*(8*x3)*(1)+3*(4*x2)*(−3)+3*(2*x)*(9)+1*(1)*(−27)

5. Multiply the coefficients and constants to simplify each term.

8*x3−36*x2+54*x−27

Final Answer

(2*x−3)3=8*x3−36*x2+54*x−27

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