Question

Factorise:2a^2(b^2-c^2)+b^2(2c^2-2a^2)+2c^2(a^2-b^2)​

Answer 1

Question=2a²(b²-c²)+2b²(c²-a²)+2c²(a²-b²)

It is A Homogeneous Expression With Multiple Variable

So Should u do First Common Similar thing

2[a²(b²-c²)+b²(c²-a²)+c²(a²-b²)]

Now See Say b=-c

2[a²(c²-c²)+c²(c²-a²)+c²(a²-c²)]

=0

Means b=-c and It is A root so

(b+c) can Be one Factor

and it is a Homogeneous Expression then (c+a)(a+b) is also a root

now

2[(a+c)(c+a)(b+a)]

if it is Right thanks me

Answer 2

$\cancel{2}a^{2}b ^{2} - \cancel 2 {a}^{2} {c}^{2} \cancel+ 2 {b}^{2} {c}^{2} \cancel- 2 {a}^{2} {b}^{2} \cancel+ 2 {a}^{2} {c}^{2} \cancel - 2 {b}^{2} {c}^{2} \\ \\ 0$