What is factor (5x-2)^3-8 ?

The solution to factor (5x-2)^3-8 is (5x-4)(25x^2-10x+4)

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factor (5x-2)^3-8

factor

(5 x - 2)^{3} - 8

(5 x - 4) (25 x^{2} - 10 x + 4)

Solution steps

(5 x - 2)^{3} - 8

Rewrite

8

2^{3}

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

Apply Difference of Cubes Formula:

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

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

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

Refine

= (5 x - 4) ((5 x - 2)^{2} + 2 (5 x - 2) + 4)

Expand

(5 x - 2)^{2} + 2 (5 x - 2) + 4 : 25 x^{2} - 10 x + 4

= (5 x - 4) (25 x^{2} - 10 x + 4)

2 m^{2} + 2 m + m n^{'} n

3^{2} - 8 x + 4

\frac{d}{d t} ((θ) (sin (θ)))

- 2 + (- 4)

\frac{m ^{2} - 9}{3 m - 9}

What is factor (5x-2)^3-8 ?
The solution to factor (5x-2)^3-8 is (5x-4)(25x^2-10x+4)