Question

Solve the question : (i) a^4 − b^4 (ii) p^4 − 81 (iii) x^4 − (y + z)^4

Answer 1

$\bold{ \: Used \: \: Identity \: \: ( In \: All ) \: \: \: : ( a )^{2} - ( b )^{2} = ( a + b ) ( a - b ) }$





( i ) :
$\bold{ \: {a}^{4} - {b}^{4} } \\ \\ \\ \bold{ \: { ({a}^{2}) }^{2} - {({b}^{2}})^{2} } \\ \\ \\ \bold{( \:{a}^{2} - {b}^{2})( {a}^{2} + {b)}^{2} } \\ \\ \\ \bold{ \: (a + b)(a - b)( {a}^{2} + {b}^{2} ) }$





( ii ) :


$\bold{ \: {p}^{4} - 81} \\ \\ \\ \bold{ \: \: ({p}^{2} )^{2} - {( {3}^{2} )}^{2} } \\ \\ \\ \bold{( {p}^{2} - {3}^{2})( {p}^{2} + {3}^{2} ) \: \: \: } \\ \\ \\ \bold{ (p + 3)(p - 3)( {p}^{2} + 9)\: \: }$




( iii ) :


$\bold{ {x}^{4} - {(y + z)}^{4} } \\ \\ \\ \bold{( {x}^{2} )^{2} - {({y + z^{2}})}^{2} \: \: } \\ \\ \\ \bold{ \: ( {x}^{2} - (y + z) ^{2})( {x}^{2} + (y + z) ^{2} )\: } \\ \\ \\ \bold{ \:(x + y + z)(x - y - z)( {x}^{2} + {y}^{2} + {z}^{2} + 2yz) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: | {(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab}$