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GCD of Polynomials

State whether...

Question

State whether True or False.
The H.C.F. and L.C.M. of:

$x^{2} - y^{2}$ and $x^{2} - x y$ is $x - y; x (x + y) (x - y)$
If true then enter $1$ and if false then enter $0$

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Solution

Factorizing $x^{2} - y^{2}$ and $x^{2} - x y,$
$x^{2} - y^{2} = (x - y) (x + y)$
$x^{2} - x y = x (x - y)$
H.C.F. $= (x - y)$
L.C.M. $= x (x + y) (x - y)$

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