Question

factorise the following identity a6+b6

Answer 1

Hello dear,

${a}^{6} + {b}^{6} \\ \\ = > {( {(a)}^{2}) }^{3} + {( ({b)}^{2}) }^{3} \\ \\ = > {({a}^{2} + {b}^{2}) }^{3} \\ \\ as \: \: we \: \: know \: \\ (a + b {)}^{3} = {a}^{3} + {b}^{3} + 3ab( a+b ) \\ \\ = > { ({a}^{2} + {b}^{2} )}^{3} = {( {(a)}^{2} )}^{3} + {( {(b)}^{2}) }^{3} + 3 \times {a}^{2} \times {b}^{2} + ( {a}^{2} + {b}^{2} ) \\ \\ = > {a}^{6} + {b}^{6} + 3 {a}^{2} {b}^{2} + ( {a}^{2} + {b}^{2} )$

Answer 2

$Bonjour! \\ \\ = > {a}^{6} + {b}^{6} \\ \\ = > ( { {a}^{2}) }^{3} + { ({b}^{2} )}^{3} \\ \\ = > ( {a}^{2} + {b}^{2} )(( { {a}^{2}) }^{2} - {a}^{2} {b}^{2} + {( {b}^{2} )}^{2} ) \\ \\ = > ( {a}^{2} + {b}^{2} )( {a}^{4} - {a}^{2} {b}^{2} + {b}^{4} ) \\ \\ (identity \: used - - - > {x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} )) \\ \\ = > Hope \: this \: helps...:)$