Question

Factorization of the polynomial (x-y)^2a^2+2(x-y)(x+y)ab+(x+y)^2b^2 gives

Answer 1

Hey mate!

Here's your answer!!

There are 2 solutions possible...

1) Substitute a(x-y) = m AND b(x+y) = n

Now given equation re-writes as m² + 2mn + n².

The re-written equation factotises as (m+n)², or we can say there is only one factor (m+n).

Now, substitute back the values of m and n.

The single factor of the given equation is

➡ {a(x-y) + b(x+y)}.

2) This is if the form A² + 2AB + B² = (A+B)²

Where A = a(x-y) , B = b(x+y)

Hence the factors are..

[ a(x-y) + b(x+y) ]² or

[ a(x-y) + b(x+y) ][ a(x-y) + b(x+y) ]

$hope \: it \: helps \: you....$
✌ ✌

Answer 2

Let's assume 
$[x-y]a=m \\ [x+y]b=n$

Now the polynomial can be written as
$= m^{2}+2mn+ n^{2} \\ = [m+n]^{2}$

So the factor is [m+n]
=[(x+y)a + (x-y)b]