What is (x^3-6x^2+12x-8)/(x^2-4x+4) ?

The solution to (x^3-6x^2+12x-8)/(x^2-4x+4) is x-2

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simplify (x^3-6x^2+12x-8)/(x^2-4x+4)

simplify

\frac{x ^{3} - 6 x ^{2} + 12 x - 8}{x ^{2} - 4 x + 4}

x - 2

Solution steps

\frac{x ^{3} - 6 x ^{2} + 12 x - 8}{x ^{2} - 4 x + 4}

Apply cube of difference rule:

x^{3} - 3 x^{2} y + 3 x y^{2} - y^{3} = (x - y)^{3}

x^{3} - 6 x^{2} + 12 x - 8 = (x - 2)^{3}

= \frac{( x - 2 ) ^{3}}{x ^{2} - 4 x + 4}

Factor

x^{2} - 4 x + 4 : (x - 2)^{2}

= \frac{( x - 2 ) ^{3}}{( x - 2 ) ^{2}}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(x - 2)^{3} = (x - 2)^{2} (x - 2)

= \frac{( x - 2 ) ^{2} ( x - 2 )}{( x - 2 ) ^{2}}

Cancel the common factor:

(x - 2)^{2}

= x - 2

\frac{56}{10}

- y^{2} + 17 y - 72

2 i \cdot 7 i

1063

What is (x^3-6x^2+12x-8)/(x^2-4x+4) ?
The solution to (x^3-6x^2+12x-8)/(x^2-4x+4) is x-2