Question

(ax+by)2 + (bx-ay)2​

Answer 1

Answer:

(ax+by)(2)+(bx−ay)(2)

Distribute:

=(ax)(2)+(by)(2)+(bx)(2)+(−ay)(2)

=2ax+2by+2bx+−2ay

Answer:

=2ax−2ay+2bx+2by

Step-by-step explanation:

Answer 2

Answer:

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

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

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

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