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

The solution to factor (5x+1)^3-1^3 is 5x(25x^2+15x+3)

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factor (5x+1)^3-1^3

factor

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

5 x (25 x^{2} + 15 x + 3)

Solution steps

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

Apply Difference of Cubes Formula:

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

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

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

Refine

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

Expand

(5 x + 1)^{2} + 5 x + 1 + 1 : 25 x^{2} + 15 x + 3

= 5 x (25 x^{2} + 15 x + 3)

(-) n^{3}

2 x^{2 - 6 x}

15 x^{2} \cdot x^{2}

\frac{\frac{- 13}{7}}{2}

1262 cos (500 π x) + 250

What is factor (5x+1)^3-1^3 ?
The solution to factor (5x+1)^3-1^3 is 5x(25x^2+15x+3)