Factor a^3+125

Problem

a^3+125

Solution

1. Identify the expression as a sum of two cubes, which follows the form x^3+y^3

2. Rewrite the constant term as a cube to identify the base values.

125=5^3

3. Apply the formula for the sum of cubes, which is x^3+y^3=(x+y)*(x^2−x*y+y^2)

4. Substitute x=a and y=5 into the formula.

(a+5)*(a^2−(a)*(5)+5^2)

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

(a+5)*(a^2−5*a+25)

Final Answer

a^3+125=(a+5)*(a^2−5*a+25)

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