Simplify (3+h)^3

Problem

(3+h)3

Solution

1. Identify the expression as a binomial raised to the third power, which follows the pattern (a+b)3

2. Apply the formula for the cube of a binomial: (a+b)3=a3+3*a2*b+3*a*b2+b3

3. Substitute a=3 and b=h into the formula.

4. Calculate the first term: 3=27

5. Calculate the second term: 3*(3)*(h)=3*(9)*(h)=27*h

6. Calculate the third term: 3*(3)*(h2)=9*h2

7. Calculate the fourth term: h3

8. Combine all the terms into a single polynomial expression.

Final Answer

(3+h)3=27+27*h+9*h2+h3

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