Question

using identities factorise the following:
1. 9y2-66yz+121z2 (after i.e., xyz those are squares not numbers)
2.(x2-1) (x4+x2+1)

Answer 1

1. Using identity 

( a - b )² = a² + b² - 2ab,

⇒( 3 y - 11 z ) ² = 9 y ² + 121 z ² - 66 yz
⇒9 y ² + 121 z ² - 66 yz =9 y ² + 121 z ² - 66 yz

L.H.S. = R.H.S

Answer 2

9 y² - 66 y z + 121 z²
 = (3y)² - 2 * 3 y * 11 z + 11² z²
  = (3 y - 11 z)²

the identity used is    a² - 2 a b + b²  = (a - b)²
=============
x⁴ + x² + 1  = y² + y + 1        if  y = x²

we know that  (a - b) (a² + a b + b²) = a³ - b³
             or,  (y - 1) ( y² + 1 * y + 1²) = y³ - 1³

(x² - 1) * (x⁴ + x² + 1)
   = (x⁶ - 1)