What is factor (2x-5)^3-1 ?

The solution to factor (2x-5)^3-1 is 2(x-3)(4x^2-18x+21)

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factor (2x-5)^3-1

factor

(2 x - 5)^{3} - 1

2 (x - 3) (4 x^{2} - 18 x + 21)

Solution steps

(2 x - 5)^{3} - 1

Rewrite

1

1^{3}

= (2 x - 5)^{3} - 1^{3}

Apply Difference of Cubes Formula:

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

(2 x - 5)^{3} - 1^{3} = ((2 x - 5) - 1) ((2 x - 5)^{2} + (2 x - 5) + 1)

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

Refine

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

Factor

2 x - 6 : 2 (x - 3)

= 2 (x - 3) (2 x + (2 x - 5)^{2} + 1 - 5)

Expand

(2 x - 5)^{2} + 2 x - 5 + 1 : 4 x^{2} - 18 x + 21

= 2 (x - 3) (4 x^{2} - 18 x + 21)

(\frac{x}{4})^{2} - 255

(200 x^{0.21}) + (0.14 x^{300})

2 am + 6 a - bm - 3 b

ln (1 - e^{2})

x (\frac{d ^{3} y}{d x ^{3}})

What is factor (2x-5)^3-1 ?
The solution to factor (2x-5)^3-1 is 2(x-3)(4x^2-18x+21)