Question

Factorise a^8 - 81y^4

Answer 1

Answer:

(a^4 + 9y^8)(a^2 + 3y^2)(a^2 + 3y^2)

Answer 2

$Given \: a^{8} - 81y^{4}$

$= (a^{4})^{2} - (9y^{2})^{2}$

/* By algebraic identity */

$\boxed{\pink{ m^{2} - n^{2} = (m+n)(m-n) }}$

$= (a^{4} + 9y^{2})(a^{4} - 9y^{2})$

$= (a^{4} + 9y^{2})[(a^{2})^{2} - (3y)^{2}]$

$= (a^{4} + 9y^{2})(a^{2} + 3y)(a^{2} - 3y)$

Therefore.,

$\red{ Factors \: of \:a^{8} - 81y^{4}}$

$\green { = (a^{4} + 9y^{2})(a^{2} + 3y)(a^{2} - 3y)}$

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