Question

a⁴ – (b+c)⁴, Factorise the expression.

Answer 1

Solution :

a⁴ - ( b + c )⁴

= ( a² )² - [ ( b + c )² ]²

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By algebraic identity :

x² - y² = ( x + y )( x - y )

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= [ a² + ( b + c )² ] [ a² - ( b + c )² ]

= ( a² + b² + c² + 2bc ){ [a+(b+c)][a-(b+c)]}

=( a²+b²+c²+2bc )( a+b+c )( a-b-c )

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Answer 2

a⁴ - ( b + c )⁴

( a² )² - { ( b + c )² }²


• By using : ( a )² - ( b )² = ( a + b )( a - b )


{ a² - ( b + c )² }{ a² + ( b + c )² }


• By using : ( a + b )² = a² + b² + 2ab


[ ( a )² - { b + c }² ][ a² + ( b² + c² + 2bc ) ]


[ { a - ( b + c ) }{ a + ( b + c ) } ][ a² + b² + c² + 2bc ]


( a - b - c )( a + b + c )( a² + b² + c² + 2bc )



Factoized.




Therefore, a⁴ - ( b + c )⁴ = ( a - b - c )( a + b + c )( a² + b² + c² + 2bc )

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