Question

factorise the expression P ^ 4 - 81​

Answer 1

${p}^{4} - 81 \\ {( {p}^{2}})^{2} - {9}^{2} \\ using \: formula \: {a}^{2} - {b}^{2} = (a + b)(a - b) \\ {p}^{4} - 81 = ({p}^{2} + 9)( {p}^{2} - 9) \\ now \: {p}^{2} - 9 \: can \: be \: expanded \: as \: below \\ {p}^{2} - 9 = ( {p})^{2} - {3}^{2} \\ {p}^{2} - 9 = (p + 3)(p - 3) \\ therefore \: {p}^{4} - 81 = ( {p}^{2} + 9)((p + 3)(p - 3))$

Answer 2

$\bold{HERE\:IS\:YOUR\:ANSWER\::-}$

${( {p}^{2}) }^{2} - ({9})^{2} \\ ( {p}^{2} - 9)( {p}^{2} + 9) \\ ( {p}^{2} - {3}^{2} )( {p}^{2} + 9 ) \\ (p - 3)(p + 3)( {p}^{2} + 9) = > ans$
$identitiy \: used \: = > ( {a}^{2} - {b}^{2} )= (a - b)(a + b)$