What is factor (2x-5)^3-216 ?

The solution to factor (2x-5)^3-216 is (2x-11)(4x^2-8x+31)

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factor (2x-5)^3-216

factor

(2 x - 5)^{3} - 216

(2 x - 11) (4 x^{2} - 8 x + 31)

Solution steps

(2 x - 5)^{3} - 216

Rewrite

216

6^{3}

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

Apply Difference of Cubes Formula:

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

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

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

Refine

= (2 x - 11) ((2 x - 5)^{2} + 6 (2 x - 5) + 36)

Expand

(2 x - 5)^{2} + 6 (2 x - 5) + 36 : 4 x^{2} - 8 x + 31

= (2 x - 11) (4 x^{2} - 8 x + 31)

5 g df - 10 g df

\cdot (\cdot + 4 y)

121 a^{2 x} - 9 b^{4 x}

\frac{x ^{4}}{x ^{3} + 1}

- 5 w + (- 4)

What is factor (2x-5)^3-216 ?
The solution to factor (2x-5)^3-216 is (2x-11)(4x^2-8x+31)