Question

(ax + by)² + (bx - ay)²

plz answer it ​

Answer 1

Answer:

By using the formula (a+b)

2

and(a−b)

2

'we get,

=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

Rearranging the terms

=a

2

x

2

+b

2

x

2

+b

2

y

2

+a

2

y

2

By taking the common terms out

=x

2

(a

2

+b

2

)+y

2

(a

2

+b

2

)

So we get,

(ax+by)

2

+(bx−ay)

2

= (a

2

+b

2

)(x

2

+y

2

)

Answer 2

$\huge \mathfrak \purple {answer}$

(ax + by)² + (bx -ay)²

=a²x² +b²y² +2abxy +b²x² +a²y² -2abxy

= a²x² + b²x² + b²y² + a²y²

=x² (a² + b²) + y²(a²+ b²)

= (a² + b²) (x² + y²)