Question
Factorise:
$ (a x+b y)^2+(b x-a y)^2$
$ (a x+b y)^2+(b x-a y)^2$
✓
Answer
$ (a x+b y)^2+(b x-a y)^2$
$= (a^2 x^2+b^2 y^2+2 a x b y+b^2 x^2+a^2 y^2-2 b x a y$
$=a^2 x^2+b^2 y^2+b^2 x^2+a^2 y^2$
$=a^2 x^2+b^2 x^2+a^2 y^2+b^2 y^2$
$= x^2\left(a^2+b^2\right)+y^2\left(a^2+b^2\right)$
$=\left(a^2+b^2\right)\left(x^2+y^2\right) $
$= (a^2 x^2+b^2 y^2+2 a x b y+b^2 x^2+a^2 y^2-2 b x a y$
$=a^2 x^2+b^2 y^2+b^2 x^2+a^2 y^2$
$=a^2 x^2+b^2 x^2+a^2 y^2+b^2 y^2$
$= x^2\left(a^2+b^2\right)+y^2\left(a^2+b^2\right)$
$=\left(a^2+b^2\right)\left(x^2+y^2\right) $
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