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

The solution to factor (x+5)^3-(2x+1)^3 is (-x+4)(7x^2+25x+31)

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factor (x+5)^3-(2x+1)^3

factor

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

(- x + 4) (7 x^{2} + 25 x + 31)

Solution steps

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

Apply Difference of Cubes Formula:

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

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

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

Refine

= (- x + 4) ((2 x + 1)^{2} + (x + 5) (2 x + 1) + (x + 5)^{2})

Expand

(x + 5)^{2} + (2 x + 1) (x + 5) + (2 x + 1)^{2} : 7 x^{2} + 25 x + 31

= (- x + 4) (7 x^{2} + 25 x + 31)

3^{2} + 6^{2}

ln (\frac{4}{3})

lo g_{4} (8) = x

3 (2)^{2} - 3

(4 x - 3) \frac{28 x - 19}{4 x - 3} \leq 0

What is factor (x+5)^3-(2x+1)^3 ?
The solution to factor (x+5)^3-(2x+1)^3 is (-x+4)(7x^2+25x+31)