Question

(a^2+b^2-4c^2)^2-4a^2b^2

Answer 1

$(a^{2}+ b^{2} - c^{2} )^{2} -4 a^{2} b^{2}$

could also be written as:
$(a^{2}+ b^{2} - c^{2} )^{2} -(2ab)^{2}$


As you can see It is in the form of a^2 -b^2
and as
$a^{2} - b^{2} =(a+b)(a-b)$

Therefore, by using this identity you'll get

[tex]= (a^{2}+ b^{2} - c^{2} -2ab) (a^{2}+ b^{2} - c^{2}+ 2ab ) [/tex]

$(a^{2}+ b^{2}-2ab - c^{2} ) (a^{2}+ b^{2}+2ab - c^{2} )$


$((a- b)^{2} - c^{2} ) ((a+ b)^{2} - c^{2} )$


you can see that we need to use the same identity of a^2 -b^2 again

so, the whole thing becomes,
[tex] (a- b-c) (a-b+c) (a+ b-c)(a+b-c)[/tex]