What is factor (a-b)^3-27 ?

The solution to factor (a-b)^3-27 is (a-b-3)((a-b)^2+3(a-b)+9)

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factor (a-b)^3-27

factor

(a - b)^{3} - 27

(a - b - 3) ((a - b)^{2} + 3 (a - b) + 9)

Solution steps

(a - b)^{3} - 27

Rewrite

27

3^{3}

= (a - b)^{3} - 3^{3}

Apply Difference of Cubes Formula:

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

(a - b)^{3} - 3^{3} = ((a - b) - 3) ((a - b)^{2} + 3 (a - b) + 3^{2})

= ((a - b) - 3) ((a - b)^{2} + 3 (a - b) + 3^{2})

Refine

= (a - b - 3) ((a - b)^{2} + 3 (a - b) + 9)

8 cosh (ln (x)) + 4 sinh (ln (x))

[(4 y^{2} - 3) + z]^{2}

\frac{e ^{3} - e}{2}

[2.6]

What is factor (a-b)^3-27 ?
The solution to factor (a-b)^3-27 is (a-b-3)((a-b)^2+3(a-b)+9)