Question

Prove the polynomial
(x²-1)³ = x⁶-3x⁴+3x²-1

Answer 1

(x² - 1)³ = x⁶- 3x⁴ + 3x² - 1

LHS :

We know that ( a - b )³ = ( a - b ) ( a - b )² .

( x² - 1 )³ = ( x² - 1 ) ( x² - 1 )²      { ( a - b )² = a² + b² - 2ab }

= ( x² - 1 ) ( x⁴ + 1 - 2x² )

= x⁶ + x² - 2x⁴ - x⁴ - 1 + 2x²

= x⁶ - 3x⁴ + 3x² - 1

Hence , LHS = RHS .

Answer 2

Step-by-step explanation:

using identity

(a-b) ^3= a^3 - b^3 - 3a^2b + 3ab^2

Solving L. H. S=

(x^2-1)^3

= (x^2)^3 - 1^3 - 3(x^2)^2+ 3(x^2)(1)^2

=x^6 - 1 - 3x^4 + 3x^2

=x^6 - 3x^4 + 3x^2 - 1

HENCE ,

L.H.S=R.H.S