Question

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

Answer 1

Answer:

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

Step-by-step explanation:

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

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

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

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

a^2x^2+b^2y^2+b^2x^2+a^2y^2

a^2x^2+b^2x^2+b^2y^2+a^2y^2

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

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

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Answer 2

Answer:

(a² + b²) (x² + y²)

Step-by-step explanation:

(ax+by)² + (bx-ay)²

We can use formula: (a²+2ab+b²) + (a²-2ab+b²)

[(ax)² + 2(ax)(by) + (by)²] + [(bx)² - 2(bx)(ay) + (ay)²]

[a²x² + 2abxy + b²y²] + [b²x² - 2abxy + a²y²]

a²x² + a²y² + b²y² + b²x²

a²(x² + y²) +b²(y² + x²)

(a² + b²) (x² + y²)