Question

factorise (ax + by)² + (bx - ay)²​

Answer 1

Explanation:

..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

)

Answer 2

$(ax + {by)}^{2} + (bx - {ay)}^{2}$

$\\ = > {a}^{2} {x}^{2} + {b}^{2} {y}^{2} + 2axby + {b}^{2} {x}^{2} + {a}^{2} {y}^{2} - 2bxay$

$= > {a}^{2} {x}^{2} + {b}^{2} {y}^{2} + {b}^{2} {x}^{2} + {a}^{2} {y}^{2}$

$= > {x}^{2} ( {a}^{2} + {b}^{2} ) + {y}^{2} ( {a}^{2} + {b}^{2} )$

$= > ( {x}^{2} + {y}^{2} )( {a}^{2} + {b}^{2} )$

I hope this will help you dear..

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