Question
Factorise the following:$4xy - x^2 - 4y^2 + z^2$
✓
Answer
$4xy - x^2 - 4y^2 + z^2$
$= z^2 - x^2 - 4y^2 + 4xy$
$= z^2 - (x^2 + 4y^2 - 4xy)$
$= z^2 - (x - 2y)^2$
$= [z - (x - 2y)][z + (x - 2y)]$
$= (z - x + 2y)(z + x - 2y).$
$= z^2 - x^2 - 4y^2 + 4xy$
$= z^2 - (x^2 + 4y^2 - 4xy)$
$= z^2 - (x - 2y)^2$
$= [z - (x - 2y)][z + (x - 2y)]$
$= (z - x + 2y)(z + x - 2y).$
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