What is factor (3x-2)^3-27 ?

The solution to factor (3x-2)^3-27 is (3x-5)(9x^2-3x+7)

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factor (3x-2)^3-27

factor

(3 x - 2)^{3} - 27

(3 x - 5) (9 x^{2} - 3 x + 7)

Solution steps

(3 x - 2)^{3} - 27

Rewrite

27

3^{3}

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

Apply Difference of Cubes Formula:

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

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

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

Refine

= (3 x - 5) ((3 x - 2)^{2} + 3 (3 x - 2) + 9)

Expand

(3 x - 2)^{2} + 3 (3 x - 2) + 9 : 9 x^{2} - 3 x + 7

= (3 x - 5) (9 x^{2} - 3 x + 7)

x^{2} = 3 (\frac{25}{16}) + 5 (\frac{49}{36})

\frac{x}{3} \leq - 3

(\frac{4 z ^{5} y ^{0}}{x ^{2}})^{- 3}

81 - x^{2} y^{6}

x^{2} - 1 = 23

What is factor (3x-2)^3-27 ?
The solution to factor (3x-2)^3-27 is (3x-5)(9x^2-3x+7)