Question

solve the equation $y^3 - 27 = 9y^2 - 27y$. the solution is $y = \square$.

Explanation:

Step1: Rearrange all terms to left

$y^3 - 9y^2 + 27y - 27 = 0$

Step2: Recognize perfect cube form

Notice $y^3 - 9y^2 + 27y - 27=(y-3)^3$, since $(a-b)^3=a^3-3a^2b+3ab^2-b^3$ where $a=y, b=3$

Step3: Solve for y

Set $(y-3)^3=0$, so $y-3=0$

Answer:

$3$