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factorise:

(ax+by)²+(bx-ay)²

${(a x + b y)}^{2} + (b x - a y)^{2} = {(a x)}^{2} + {(b y)}^{2} + 2 (a x) (b y) + {(b x)}^{2} + {(a y)}^{2} + (a y)^{2} - 2 (b x) (a y) = a^{2} x^{2} + b^{2} y^{2} + 2 a b x y + b^{2} x^{2} + a^{2} y^{2} - 2 a b x y = x^{2} (a^{2} + b^{2}) + y^{2} (a^{2} + b^{2}) = (a^{2} + b^{2}) (x^{2} + y^{2})$

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