Factor r^3+27

Problem

r3+27

Solution

1. Identify the expression as a sum of two cubes.

2. Rewrite the terms as cubes to identify the base values.

r3+3

3. Apply the formula for the sum of cubes, which is a3+b3=(a+b)*(a2−a*b+b2)

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

(r+3)*(r2−(r)*(3)+3)

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

(r+3)*(r2−3*r+9)

Final Answer

r3+27=(r+3)*(r2−3*r+9)

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