Factor a^3+64

Problem

a3+64

Solution

1. Identify the expression as a sum of two cubes, which follows the form x3+y3

2. Rewrite the constant term as a cube to determine the values of x and y

64=4

3. Apply the formula for the sum of cubes, which is x3+y3=(x+y)*(x2−x*y+y2)

4. Substitute x=a and y=4 into the formula.

(a+4)*(a2−(a)*(4)+4)

5. Simplify the terms inside the second set of parentheses.

(a+4)*(a2−4*a+16)

Final Answer

a3+64=(a+4)*(a2−4*a+16)

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