How do you simplify $(x³-27 )/ (x-3)$ ?

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Answer 1 · 2015-10-20T18:45:42

Use the formula for the difference of two cubes to factor the top and cancel the $x-3$ to get $x^2+3x+9$

The formula for the difference of two cubes is $a^{3}-b^{3}=(a-b)(a^2+ab+b^2)$ (check this by expanding out the right side).

Thus, since $x^3-27=x^3-3^3$ ,

$(x^3-27)/(x-3)=((x-3)(x^2+3x+9))/(x-3)=((cancel(x-3))(x^2+3x+9))/(cancel(x-3))=x^2+3x+9$

This last equality is true as long as $x!=3$ .

How do you simplify (x³-27 )/ (x-3)(x³-27 )/ (x-3)?