Question

Simplify:-
(a^2-b^2)(a^2-ab+b^2)(a^2+ab+b^2)

Answer 1

Solution :

(a² - b²) (a² - ab + b²) (a² + ab + b²)

= (a + b) (a - b) (a² - ab + b²) (a² + ab + b²)

= {(a + b) (a² - ab + b²)}

{(a - b) (a² + ab + b²)}

= (a³ + b³) (a³ - b³)

= a⁶ - b⁶ ,

which is the required simplification.

Identity Rules :

• a² - b² = (a + b) (a - b)
• a³ + b³ = (a + b) (a² - ab + b²)
• a³ - b³ = (a - b) (a² + ab + b²)
• (aⁿ + bⁿ) (aⁿ - bⁿ) = a²ⁿ - b²ⁿ

Answer 2

$\Large{\underline{\mathfrak{\underline{Solution :-}}}}$

$\sf (a {}^{2} - b {}^{2} )(a {}^{2} - ab + b {}^{2} )(a {}^{2} + ab + b {}^{2}) \\ \sf = (a - b)(a + b)(a {}^{2} - ab + b {}^{2} )(a {}^{2} + ab + b {}^{2}) \\ \sf = \{(a - b)(a {}^{2} + ab + b {}^{2}) \} \{(a + b)(a {}^{2} - ab + b {}^{2}) \} \\ \sf = (a {}^{3} - b {}^{3} )(a {}^{3} + b {}^{3} ) \\ \sf = (a {}^{6} - b {}^{6})$

____________________________________

$\sf \large Identity \: Used :$

1. (a² - b²) = (a + b)(a - b)

2. (a - b)(a² + ab + b²) = (a³ - b³)

3. (a + b)(a² - ab + b²) = (a³ + b³)

4. (a² + b²)(a² - b²) = a² - b²

____________________________________