What is factor 216(x-2)^3-(x-1)^3 ?

The solution to factor 216(x-2)^3-(x-1)^3 is (5x-11)(43x^2-164x+157)

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factor 216(x-2)^3-(x-1)^3

factor

216 (x - 2)^{3} - (x - 1)^{3}

(5 x - 11) (43 x^{2} - 164 x + 157)

Solution steps

216 (x - 2)^{3} - (x - 1)^{3}

Rewrite

216 (x - 2)^{3} - (x - 1)^{3}

(6 (x - 2))^{3} - (x - 1)^{3}

= (6 (x - 2))^{3} - (x - 1)^{3}

Apply Difference of Cubes Formula:

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

(6 (x - 2))^{3} - (x - 1)^{3} = (6 (x - 2) - (x - 1)) (6^{2} (x - 2)^{2} + 6 (x - 2) (x - 1) + (x - 1)^{2})

= (6 (x - 2) - (x - 1)) (6^{2} (x - 2)^{2} + 6 (x - 2) (x - 1) + (x - 1)^{2})

Refine

= (- x + 6 (x - 2) + 1) ((x - 1)^{2} + 6 (x - 2) (x - 1) + 36 (x - 2)^{2})

Expand

6 (x - 2) - x + 1 : 5 x - 11

= (5 x - 11) (6 (x - 2) (x - 1) + (x - 1)^{2} + 36 (x - 2)^{2})

Expand

36 (x - 2)^{2} + 6 (x - 2) (x - 1) + (x - 1)^{2} : 43 x^{2} - 164 x + 157

= (5 x - 11) (43 x^{2} - 164 x + 157)

75 x^{2} - 7 x - 2 + 0

- r^{4} + 4 y^{3} + 21 y^{3}

x^{2} + x e^{3}

x^{2} + x^{2}

(x + y)^{2} - 3 (x + y) - 4

What is factor 216(x-2)^3-(x-1)^3 ?
The solution to factor 216(x-2)^3-(x-1)^3 is (5x-11)(43x^2-164x+157)