Question

(ax+by )^2 +(bx-ay)^2​

Answer 1

question :-

$(ax + by)^2 + (bx + ay)^2$

identity used:-

$(a+b)^2 = a^2 + b^2 +2ab$

$(a-b)^2=a^2+b^2-2ab$

solution:-

$(ax + by)^2 + (bx + ay)^2$

$(ax^2+by^2+2axby)+(bx^2+ay^2-2bxay)$

$ax^2+by^2+2axby+bx^2+ay^2-2bxay$

$ax^2+by^2+bx^2+ay^2$

$ax^2+bx^2+by^2+ay^2$

$x^2(a^2+b^2)+y^2(a^2+b^2)$

$(a^2+b^2)(x^2+y^2)$

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Answer 2

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

a^2.x^2+b^2.y^2+2abxy + b^2.x^2+a^2.y^2-abxy

=>a^2.b^2+b^2.y^2 + b^2.x^2+a^2.y^2

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