Question

a x + b y ka whole square + b x minus a y ka whole square

Answer 1

Factorise :-

(ax + by)² + (bx - ay)²

Let's open the brackets first

We know that, (a + b)² = a² + b² + 2ab

=> (ax + by)² + (bx - ay)²

= a²x² + b²y² + 2axby + b²x² + a²y² - 2bxay

=> a²x² + a²y² + b²y² + b²x² + 2abxy - 2abxy

(rearranging the terms)

=> a²x² + a²y² + b²y² + b²x²

=> a²(x² + y²) + b²(x² + y²)

=> (a² + b²)(x² + y²)

Hope it helps dear friend ☺️✌️

Answer 2

Answer:

Step-by-step explanation:

As we know :-( a+b )^2 =a^2+b^2+2ab

So that

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

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

So we can cancel 2axby and -2bxay

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

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

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

Thanks

I hope it helps you