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

The solution to factor (2+x)^3-216 is (x-4)(x^2+10x+52)

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factor (2+x)^3-216

factor

(2 + x)^{3} - 216

(x - 4) (x^{2} + 10 x + 52)

Solution steps

(2 + x)^{3} - 216

Rewrite

216

6^{3}

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

Apply Difference of Cubes Formula:

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

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

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

Refine

= (x - 4) ((x + 2)^{2} + 6 (x + 2) + 36)

Expand

(2 + x)^{2} + 6 (2 + x) + 36 : x^{2} + 10 x + 52

= (x - 4) (x^{2} + 10 x + 52)

2 a c^{2} + b c^{2} - 2 a c - b c - 2 a - b

v (- 1.2)

\frac{1}{2} (ln (2))

[(x - y) + z] [(x - y) - z]

x^{2} + x y - b x - b y

What is factor (2+x)^3-216 ?
The solution to factor (2+x)^3-216 is (x-4)(x^2+10x+52)