Sum

**factorise : **(ac + by)^{2} + (bx - ay)^{2}

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#### Solution

(ax + by)^{2} + (bx - ay)^{2}

= a^{2}x^{2} + b^{2}y^{2} + 2abxy + b^{2}x^{2} + a^{2}y^{2} - 2abxy

= a^{2}x^{2} + b^{2}y^{2} + b^{2}x^{2} + a^{2}y^{2}

= a^{2}x^{2} + a^{2}y^{2} + b^{2}x^{2} + b^{2}y^{2}

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

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

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