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

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Solution

Find Factors of $a b (x^{2} + y^{2}) - x y (a^{2} + b^{2})$
Simplify the function by taking $b x, a y$ common.
$a b x^{2} - x y b^{2} + a b y^{2} - x y a^{2} = b x (a x - y b) - a y (a x - b y)$
$= (b x - a y) (a x - b y)$
Hence the answer is $(b x - a y) (a x - b y)$

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Q. Factorize

a b (x^{2} + y^{2}) - x y (a^{2} + b^{2})

Q. Solve :

a b (x^{2} + y^{2}) - x y (a^{2} + b^{2})

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Factorize ab(x2+y2)−xy(a2+b2)

Find Factors of abx2+y2-xya2+b2Simplify the function by taking bx,ay common.abx2-xyb2+aby2-xya2=bxax-yb-ayax-by=bx-ayax-byHence the answer is bx-ayax-by

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

Find Factors of $a b (x^{2} + y^{2}) - x y (a^{2} + b^{2})$
Simplify the function by taking $b x, a y$ common.
$a b x^{2} - x y b^{2} + a b y^{2} - x y a^{2} = b x (a x - y b) - a y (a x - b y)$
$= (b x - a y) (a x - b y)$
Hence the answer is $(b x - a y) (a x - b y)$