Question

factorise (ax+by)² + (bx-ay)²​

Answer 1

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$\huge\bf{Question:-}$

Factorise (ax+by)² + (bx-ay)²

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$\huge\bf{Solution:-}$

(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)

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Answer 2

Answer:

Given : (ax+by)

2

+(bx−ay)

2

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

)