Question

factorise 2x⁷-128x answer is 2x(x-2)(x+2)(x²+2x+4)(x²-2x+4)​

Answer 1

Answer:

Factorise: x^2+1/x^2+2-2x-2/x

Asked by aahnik.mohanty | 25th Dec, 2017, 09:54: AM

Expert Answer:

begin mathsize 16px style straight x squared plus 1 over straight x squared plus 2 minus 2 straight x minus 2 over straight x

equals open parentheses straight x squared plus 1 over straight x squared plus 2 close parentheses minus 2 open parentheses straight x plus 1 over straight x close parentheses

equals open parentheses straight x plus 1 over straight x close parentheses squared minus 2 open parentheses straight x plus 1 over straight x close parentheses

equals open parentheses straight x plus 1 over straight x close parentheses open parentheses straight x plus 1 over straight x close parentheses minus 2 open parentheses straight x plus 1 over straight x close parentheses

equals open parentheses straight x plus 1 over straight x close parentheses open parentheses straight x plus 1 over straight x minus 2 close parentheses end style

Answer 2

Answer:

2x (x - 2) (x + 2) (x² + 2x + 4) (x² - 2x +4)

Step-by-step explanation:

We know that,

a³ - b² = (a - b)(a² + ab + b²)

a³ + b³ = (a + b)(a² - ab + b²)

a² - b² = (a + b)(a - b)

$\red{\underline \bold \green {Factorisation : }}$

2x⁷ - 128x

= 2x (x⁶ - 64)

= 2x { (x³)² - (8)² }

= 2x (x³ - 8) (x³ + 8)

= 2x { (x)³ - (2)³ } { (x)³ + (2)³ }

= 2x { (x - 2)(x² + 2x + 2²) } { (x + 2)(x² - 2x + 2²) }

= 2x { (x - 2)(x² + 2x + 4) } { (x + 2)(x² - 2x + 4) }

= 2x (x - 2) (x + 2) (x² + 2x + 4) (x² - 2x +4)