What is factor 8(x-2)^3-27(x+1)^3 ?

The solution to factor 8(x-2)^3-27(x+1)^3 is -(x+7)(19x^2-4x+13)

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factor 8(x-2)^3-27(x+1)^3

factor

8 (x - 2)^{3} - 27 (x + 1)^{3}

- (x + 7) (19 x^{2} - 4 x + 13)

Solution steps

8 (x - 2)^{3} - 27 (x + 1)^{3}

Rewrite

8 (x - 2)^{3} - 27 (x + 1)^{3}

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

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

Apply Difference of Cubes Formula:

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

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

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

Refine

= (2 (x - 2) - 3 (x + 1)) (9 (x + 1)^{2} + 6 (x + 1) (x - 2) + 4 (x - 2)^{2})

Factor

2 (x - 2) - 3 (x + 1) : - (x + 7)

= (- (x + 7)) (9 (x + 1)^{2} + 6 (x + 1) (x - 2) + 4 (x - 2)^{2})

Remove parentheses:

(- a) = - a

= - (x + 7) (9 (x + 1)^{2} + 6 (x + 1) (x - 2) + 4 (x - 2)^{2})

Expand

9 (x + 1)^{2} + 6 (x + 1) (x - 2) + 4 (x - 2)^{2} : 19 x^{2} - 4 x + 13

= - (x + 7) (19 x^{2} - 4 x + 13)

x (2 x + 9) - 11

cosh (I n (x)) - sinh (I n (x))

49 x 6 - 70 a x 3 n 2 + 25 a 2 n 4

100 - y^{8}

(2 x - 1) 2 - 49

What is factor 8(x-2)^3-27(x+1)^3 ?
The solution to factor 8(x-2)^3-27(x+1)^3 is -(x+7)(19x^2-4x+13)