Question

factorise (ax+by)^2+(ax-by)^2​

Answer 1

Answer:

(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

)