Question

FACTORIZE
(a) (2x+2/x)^3
(b) (4/5x-2)^3
​

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Answer:

Step-by-step explanation:

A.((4 x)/5 - 2)^3

B.(2 x + 2/x)^3

Plots:

Plots

Plots

Alternate forms:

(8 (x^2 + 1)^3)/x^3

8 x^3 + 8/x^3 + 24 x + 24/x

Complex roots:

x = -i

x = i

Roots in the complex plane:

Roots in the complex plane

Properties as a real function:

{x element R : x!=0}

Range

{y element R : y<=-64 or y>=64}

Parity

odd

Series expansion at x = 0:

8/x^3 + 24/x + 24 x + O(x^2)

(Laurent series)

Series expansion at x = ∞:

8 x^3 + 24 x + 24/x + O((1/x)^2)

(Laurent series)

Derivative:

d/dx((2 x + 2/x)^3) = (24 (x^2 - 1) (x^2 + 1)^2)/x^4

Indefinite integral:

integral(2/x + 2 x)^3 dx = 2 (x^4 + 6 x^2 - 2/x^2 + 12 log(x)) + constant

(assuming a complex-valued logarithm)

Local maximum:

max{(2 x + 2/x)^3} = -64 at x = -1

Local minimum:

min{(2 x + 2/x)^3} = 64 at x = 1

Series representations:

(2/x + 2 x)^3 = sum_(n=-∞)^∞ ( piecewise | 8 | (n = -3 or n = 3)

24 | (n = -1 or n = 1)) x^n

(2/x + 2 x)^3 = sum_(n=-∞)^∞ ( piecewise | 4 (-1)^n (8 + 3 n + n^2) | n>3

96 | n = 2

64 | n = 0

-96 | n = 3) (-1 + x)^n

Integral representation:

(1 + z)^a = ( integral_(-i ∞ + γ)^(i ∞ + γ) (Γ(s) Γ(-a - s))/z^s ds)/((2 π i) Γ(-a)) for (0<γ<-Re(a) and abs(arg(z))<π)