Question
Factorise:$4x^4 + 25y^4 + 19x^2y^2$
✓
Answer
$4x^4 + 25y^4 + 19x^2y^2$
$= 4x^4 + 25y^4 + 20x^2y^2 - x^2y^2$
$= (2x^2)^2 + (5y^2)^2 + 2 x (2x^2) x (5y^2) - x^2y^2$
$= [(2x^2)^2 + (5y^2) + 2 x (2x^2) x (5y^2)] -x^2y^2$
$= [2x^2 + 5y^2] - (xy)^2$
$= (2x^2 + 5y^2 - xy)(2x^2 - 5y + xy).$
$= 4x^4 + 25y^4 + 20x^2y^2 - x^2y^2$
$= (2x^2)^2 + (5y^2)^2 + 2 x (2x^2) x (5y^2) - x^2y^2$
$= [(2x^2)^2 + (5y^2) + 2 x (2x^2) x (5y^2)] -x^2y^2$
$= [2x^2 + 5y^2] - (xy)^2$
$= (2x^2 + 5y^2 - xy)(2x^2 - 5y + xy).$
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