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Question
Factorize each of the following expression:
(ax + by)2 + (bx − ay)2
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Solution
\[(ax + by )^2 + (bx - ay )^2 = a^2 x^2 + 2abxy + b^2 y^2 + b^2 x^2 - 2abxy + a^2 y^2 \]
\[ = a^2 x^2 + b^2 y^2 + b^2 x^2 + a^2 y^2 \]
\[ = ( a^2 x^2 + a^2 y^2 ) + ( b^2 x^2 + b^2 y^2 ) \][Regrouping the expressions]
\[ = a^2 ( x^2 + y^2 ) + b^2 ( x^2 + y^2 )\]
\[ = ( a^2 + b^2 )( x^2 + y^2 )\] [Taking \[( x^2 + y^2 )\] as the common factor]
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