Question

factorise x to the power 4 - 81 Y to the power 4

Answer 1

${x}^{4} - {81 \: y}^{4}$

$= (x {}^{2} ) {}^{2} - (9y {}^{2} ) {}^{2}$

Using identity -

a^2 - b^2 = (a+b)(a-b)


$= (x {}^{2} + 9y {}^{2} )( {x}^{2} - 9y {}^{2} )$



Again


$= (x {}^{2} + {9y}^{2} )(x {}^{2} - (3y) {}^{2})$


$= (x {}^{2} + y {}^{2} )(x + 3y)(x - 3y)$


$\bf{Hope\:it\:helps}$