a⁴ -(b+c)⁴ factorise
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a⁴ - ( b + c )⁴
= ( a² )² - [ ( b + c )² ]²
*********************************
By algebraic identity :
x² - y² = ( x + y )( x - y )
*********************************
= [ 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 )
= ( a² )² - [ ( b + c )² ]²
*********************************
By algebraic identity :
x² - y² = ( x + y )( x - y )
*********************************
= [ 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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