What is factor (3n-2)^3-125 ?

The solution to factor (3n-2)^3-125 is (3n-7)(9n^2+3n+19)

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factor (3n-2)^3-125

factor

(3 n - 2)^{3} - 125

(3 n - 7) (9 n^{2} + 3 n + 19)

Solution steps

(3 n - 2)^{3} - 125

Rewrite

125

5^{3}

= (3 n - 2)^{3} - 5^{3}

Apply Difference of Cubes Formula:

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

(3 n - 2)^{3} - 5^{3} = ((3 n - 2) - 5) ((3 n - 2)^{2} + 5 (3 n - 2) + 5^{2})

= ((3 n - 2) - 5) ((3 n - 2)^{2} + 5 (3 n - 2) + 5^{2})

Refine

= (3 n - 7) ((3 n - 2)^{2} + 5 (3 n - 2) + 25)

Expand

(3 n - 2)^{2} + 5 (3 n - 2) + 25 : 9 n^{2} + 3 n + 19

= (3 n - 7) (9 n^{2} + 3 n + 19)

(x^{2} + 6) (x + 9)

f (x) + (- x^{2}) + 5

6 x + (- 7)

(x)^{N + 1}

4 e^{5} - 4 e^{2}

What is factor (3n-2)^3-125 ?
The solution to factor (3n-2)^3-125 is (3n-7)(9n^2+3n+19)