Question
Factorise : $4xy - x^2- 4y^2+ z^2$
✓
Answer
$4xy - x^2- 4y^2+ z^2$
$= z^2- ( x^2+ 4y^2- 4xy )$
$= z^2- ( x - 2y )^2$
$= [ z - ( x - 2y )][ z + ( x - 2y )] [ \because a^2 - b^2 = ( a + b )( a - b )]$
$= [ z - x + 2y ][ z + x - 2y ]$
$= z^2- ( x^2+ 4y^2- 4xy )$
$= z^2- ( x - 2y )^2$
$= [ z - ( x - 2y )][ z + ( x - 2y )] [ \because a^2 - b^2 = ( a + b )( a - b )]$
$= [ z - x + 2y ][ z + x - 2y ]$
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