Factorise: (ax+by)^2+(bx-ay)^2
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(ax+by)^2 + (bx - ay)^2
= a^2x^2+2abxy+b^2y^2+a^2y^2+−2abxy+b^2x^2
= a^2x^2 + a^2y^2 + b^2x^2 + b^2y^2
= a^2(x^2+y^2) + b^2(x^2+y^2)
= (a^2+b^2)(x^2+y^2)
= a^2x^2+2abxy+b^2y^2+a^2y^2+−2abxy+b^2x^2
= a^2x^2 + a^2y^2 + b^2x^2 + b^2y^2
= a^2(x^2+y^2) + b^2(x^2+y^2)
= (a^2+b^2)(x^2+y^2)
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