What is factor (x-4)^3-(2x+5)^3 ?

The solution to factor (x-4)^3-(2x+5)^3 is (-x-9)(7x^2+9x+21)

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factor (x-4)^3-(2x+5)^3

factor

(x - 4)^{3} - (2 x + 5)^{3}

(- x - 9) (7 x^{2} + 9 x + 21)

Solution steps

(x - 4)^{3} - (2 x + 5)^{3}

Apply Difference of Cubes Formula:

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

(x - 4)^{3} - (2 x + 5)^{3} = ((x - 4) - (2 x + 5)) ((x - 4)^{2} + (x - 4) (2 x + 5) + (2 x + 5)^{2})

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

Refine

= (- x - 9) ((2 x + 5)^{2} + (x - 4) (2 x + 5) + (x - 4)^{2})

Expand

(x - 4)^{2} + (x - 4) (2 x + 5) + (2 x + 5)^{2} : 7 x^{2} + 9 x + 21

= (- x - 9) (7 x^{2} + 9 x + 21)

a^{2} b^{4} c^{6} - d^{8} e^{10}

a x - 2 b x - 2 a y + 4 a y

2 cos^{2} (w) + 3 cos (w) - 5

[(6 a + b) + 4]^{2}

- (\frac{3}{2})

What is factor (x-4)^3-(2x+5)^3 ?
The solution to factor (x-4)^3-(2x+5)^3 is (-x-9)(7x^2+9x+21)