Question

factorise: (ax+by)²+(ay-bx)²
I need the procedure,,, by the way the correct answer is
(a²+b²)(x²+y²)​

Answer 1

Step-by-step explanation:

$(ax+by)²+(ay-bx)² \\ = {a}^{2} {x}^{2} + {b}^{2} {y}^{2} + 2 \times ax \times by \: + {a}^{2} {y}^{2} + {b}^{2} {x}^{2} - 2 \times ay \times bx \\ = {a}^{2} {x}^{2} + {b}^{2} {y}^{2} + 2axby + {a}^{2} {y}^{2} + {b}^{2} {x}^{2} - 2axby \\ = {a}^{2} {x}^{2} + {b}^{2} {y}^{2} + {a}^{2} {y}^{2} + {b}^{2} {x}^{2} \\ = {y}^{2} ( {a}^{2} + {b}^{2} ) + {x}^{2} ( {a}^{2} + {b}^{2} ) \\ = ( {a}^{2} + {b}^{2} ) ( {x}^{2} + {y}^{2} )$

OM NAMAH SHIVAYA

Debasish Biswal