Question

( ax + by ) ² + ( ay - bx )² factories the equation

Answer 1

# ANSWER !!

➡Factorise ..

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

Here are two terms ,

So firstly solve the first term , i.e

$( ax + by )^2$

Solve this with the identity $(a+b)^2$

$= (ax)^2 + (by)^2 + 2*ax*by$

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

Now , solve the second term ,

$( ay - bx )^2$

Solve this with the identity $(a-b)^2$

$= (ay)^2 + (bx)^2 - 2*ay*bx$

$= a^2y^2 + b^2x^2 - 2abxy$

Now join the two terms as given in the question with (+) sign..

$= a^2x^2 + b^2y^2 + 2abxy + a^2y^2 + b^2x^2 - 2abxy$

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

Thanks.....☺✌

Answer 2

$(ax+by)^2 + (ay - bx)^2 \\ = ((ax)^2 + (by)^2 + 2(ax)(by)) + ((ay)^2 + (bx)2 - 2(ay)(bx)) \\ = (a^2x^2 + b^2y^2 + 2abxy) + (a^2y^2 + b^2x^2 - 2 abxy) \\ = a^2x^2 + b^2y^2 + 2abxy + a^2y^2 + b^2x^2 - 2 abxy \\ = a^2x^2 + b^2y^2 + a^2y^2 + b^2x^2 \\ None \: of \: these \: are \: like \: terms \: ......... \\ So, \: nothing \: can \: be \: added \: or \: subtracted \: at \: this \: time...... \\ Hence, \: this \: must \: be \: the \: answer........$