Simplify (2x-3)^3

Problem

(2*x−3)^3

Solution

1. Identify the expression as a binomial cube of the form (a−b)^3

2. Apply the formula for the cube of a binomial, which is (a−b)^3=a^3−3*a^2*b+3*a*b^2−b^3

3. Substitute a=2*x and b=3 into the formula.

4. Expand the first term: (2*x)^3=8*x^3

5. Expand the second term: −3*(2*x)^2*(3)=−3*(4*x^2)*(3)=−36*x^2

6. Expand the third term: 3*(2*x)*(3^2)=3*(2*x)*(9)=54*x

7. Expand the fourth term: −(3^3)=−27

8. Combine all the expanded terms to write the final polynomial.

Final Answer

(2*x−3)^3=8*x^3−36*x^2+54*x−27

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