Simplify (x+4)^3

Problem

(x+4)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, which is (a+b)3=a3+3*a2*b+3*a*b2+b3

3. Substitute a=x and b=4 into the formula.

x3+3*(x2)*(4)+3*(x)*(4)+4

4. Simplify each term by performing the multiplication and exponentiation.

x3+12*x2+3*(x)*(16)+64

5. Combine the remaining constants to reach the final polynomial form.

x3+12*x2+48*x+64

Final Answer

(x+4)3=x3+12*x2+48*x+64

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