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=a^3+3*a^2*b+3*a*b^2+b^3

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*h^2

(h)^3=h^3

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

Final Answer

(2+h)^3=8+12*h+6*h^2+h^3

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