Factorise : 3x^7y - 81x^4y^4 - Vidyadip

Question

Factorise : $3x^7y - 81x^4y^4$

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Answer

$3x^7y - 81x^4y^4$
$= 3xy( x^6 - 27x^3y^3 )$
$= 3xy[ (x^2)^3 - ( 3xy )^3 ]$
$= 3xy( x^2 - 3xy )[ (x^2)^2 + x^2 \times 3xy + (3xy)^2 ] [ \because a^3 - b^3 = ( a -b )( a^2 + ab + b^2 )]$
$= 3xy( x^2 - 3xy )[ x^4 + 3x^3y + 9x^2y^2 ]$
$= 3xy [ x( x + 3y) x^2( x^2 + 3xy + 9y^2 ) ]$
$= 3x^4y( x - 3y )( x^2 + 3xy + 9y^2 )$

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