Question

Factories ( x6 - y6) , (a³-2√2b³),(2a7-128a ).

Answer 1

(1) ( X^6 - Y^6 )

=> ( X³ )² - ( Y³)²

=> ( X³ - Y³ ) ( X³ + Y³ )

=> ( X - Y ) ( X² + XY + Y² ) ( X + Y ) ( X² - XY + Y²).

=> ( X - Y ) ( X + Y ) ( X² + XY + Y² ) ( X² - XY + Y²).

Therefore,

( X^6 - Y^6 ) = ( X - Y ) ( X + Y ) ( X² + XY + Y² ) ( X² - XY + Y² ).

(2) a³ - 2√2b³

=> [ (a)³ - (√2b)³ ]

=> ( a - √2b ) ( a² + √2ab + 2b² )

Hence,

( a³ - 2√2b³ ) = ( a - √2b ) ( a² + √2ab + 2b²).


(3) 2a^7 - 128a


=> 2a ( a^6 - 64 )


=> 2a [ (a³)² - (8)² ]


=> 2a ( a³ + 8 ) ( a³ - 8 )


=> 2a ( a³ + 2³ ) ( a³ - 2³ )


=> 2a ( a + 2 ) ( a² - 2a + 4 ) ( a² + 2a + 4 ).


=> 2a ( a + 2 ) ( a - 2 ) ( a² + 2a + 4 ) ( a² - 2a + 4 ).

Answer 2

Heya!!
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$= > > factorize < < = \\ ............................................... \\ \\ \\ |1| .(x {}^{6} - y {}^{6} ) \\ \\ = > (x {}^{3} ) {}^{2} - (y {}^{3} ) {}^{2} \\ \\ = > ( x{}^{3} - y {}^{3} )(x {}^{3} + y {}^{3} ) \\ \\ = > > (x - y)(x {}^{2} + xy + y {}^{2} )(x + y)(x {}^{2} - xy + y {}^{2} ) \\ \\ \\ \\ = = = = = = = = = = = = = = = = = = = = = = = = = = \\ \\ \\ \\ |2| .a {}^{3} - 2 \sqrt{2} b {}^{3} \\ \\ = > (a) {}^{3} - ( \sqrt{2}b ) {}^{3} \\ \\ = > > (a - \sqrt{2} b)(a {}^{2} + \sqrt{2} ab + 2b {}^{2} ) \\ \\ \\ \\ = = = = = = = = = = = = = = = = = = = = = = = = \\ \\ \\ |3| .2a {}^{7} - 128a \\ \\ taking \: \: 2a \: common \: \\ \\ = > 2a(a {}^{6} - 64) \\ \\ = > 2a((a {}^{3} ) {}^{2} - (8) {}^{2} ) \\ \\ = > 2a(a {}^{3} + 8)(a {}^{3} - 8) \\ \\ = > > 2a(a + 2)(a-2)(a {}^{2} - 2a + 4)(a { }^{2} + 2a + 4) \\ \\ = = = = = = = = = = = = = = = = = = = = = = = = = = =$