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GCD of Polynomials

State whether...

Question

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

$a^{2} b^{2} - b^{4}, a b^{2} + b^{3}$ and $a b - b^{2}$ is $b; b^{2} (a^{2} - b^{2})$
If true then enter $1$ and if false then enter $0$

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Solution

Factorizing $a^{2} b^{2} - b^{4}, a b^{2} + b^{3}$ and $a b - b^{2},$
$a^{2} b^{2} - b^{4} = b^{2} (a^{2} - b^{2}) = b^{2} (a + b) (a - b)$
$a b^{2} + b^{3} = b^{2} (a + b)$
$a b - b^{2} = b (a - b)$
H.C.F. $= b$
L.C.M. $= b^{2} (a^{2} - b^{2})$

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