What is factor (5x-1)^3+216 ?

The solution to factor (5x-1)^3+216 is 5(x+1)(25x^2-40x+43)

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factor (5x-1)^3+216

factor

(5 x - 1)^{3} + 216

5 (x + 1) (25 x^{2} - 40 x + 43)

Solution steps

(5 x - 1)^{3} + 216

Rewrite

216

6^{3}

= (5 x - 1)^{3} + 6^{3}

Apply Sum of Cubes Formula:

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

(5 x - 1)^{3} + 6^{3} = ((5 x - 1) + 6) ((5 x - 1)^{2} - 6 (5 x - 1) + 6^{2})

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

Refine

= (5 x + 5) ((5 x - 1)^{2} - 6 (5 x - 1) + 36)

Factor

5 x + 5 : 5 (x + 1)

= 5 (x + 1) ((5 x - 1)^{2} - 6 (5 x - 1) + 36)

Expand

(5 x - 1)^{2} - 6 (5 x - 1) + 36 : 25 x^{2} - 40 x + 43

= 5 (x + 1) (25 x^{2} - 40 x + 43)

ab + a c + 3 b + 3 c

x^{2} - 2 x y + 4 x z - 8 yz

β (4.7)

98 + 42

6 x c + y d + 2 d x + 3 cy

What is factor (5x-1)^3+216 ?
The solution to factor (5x-1)^3+216 is 5(x+1)(25x^2-40x+43)