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

The solution to factor (5x+3)^3+(x-5)^3 is 14(3x-1)(3x^2+6x+7)

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

factor

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

14 (3 x - 1) (3 x^{2} + 6 x + 7)

Solution steps

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

Apply Sum of Cubes Formula:

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

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

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

Refine

= (6 x - 2) ((5 x + 3)^{2} - (x - 5) (5 x + 3) + (x - 5)^{2})

Factor

6 x - 2 : 2 (3 x - 1)

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

Factor

(5 x + 3)^{2} - (x - 5) (5 x + 3) + (x - 5)^{2} : 7 (3 x^{2} + 6 x + 7)

= 2 (3 x - 1) \cdot 7 (3 x^{2} + 6 x + 7)

Refine

= 14 (3 x - 1) (3 x^{2} + 6 x + 7)

cos^{2} (x) + 2 cos (x) - 3

3 x^{2} + 4 - 20

e^{2} - e^{3}

3 a + 3 b + a x + b x

x^{21} + 27

What is factor (5x+3)^3+(x-5)^3 ?
The solution to factor (5x+3)^3+(x-5)^3 is 14(3x-1)(3x^2+6x+7)