Factor a^3-27

Problem

a^3−27

Solution

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

2. Rewrite the terms as perfect cubes to identify x and y

a^3−27=a^3−3^3

3. Apply the formula for the difference of cubes: x^3−y^3=(x−y)*(x^2+x*y+y^2)

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

(a−3)*(a^2+(a)*(3)+3^2)

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

(a−3)*(a^2+3*a+9)

Final Answer

a^3−27=(a−3)*(a^2+3*a+9)

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