Multiply (2+h)^3

Problem

(2+h)3

Solution

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

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

3. Substitute a=2 and b=h into the formula.

(2+h)3=(2)3+3*(2)2*(h)+3*(2)*(h)2+(h)3

4. Simplify each term by calculating the powers and products.

(2)3=8

3*(2)2*(h)=3*(4)*(h)=12*h

3*(2)*(h)2=6*h2

(h)3=h3

5. Combine the simplified terms into the final polynomial expression.

Final Answer

(2+h)3=8+12*h+6*h2+h3

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