Pls help me with this equation, we must use grouping to get the answer: m^2 - 6mn + 9n^2 - 4a^2 + 4ab - b^2 (the sign "^" refers to the...

We'll create the following
groups:

(m^2 - 6mn + 9n^2) - (4a^2 - 4ab +
b^2)

We notice that within brackets, we'll have two
pwerfect squares that return the formula:

x^2 - 2xy + y^2 =
(x - y)^2

We'll manage the 1st pair of
brackets:

Let x = m and y = 3n => m^2 - 6mn + 9n^2 =
(m - 3n)^2

We'll manage the 2nd pair of
brackets:

Let x = 2a and y = b => 4a^2 - 4ab + b^2 =
(2a - b)^2

The difference between squares will
be:

(m - 3n)^2 - (2a -
b)^2

But we know that the difference between two squares
returns the product:

x^2 - y^2 =
(x-y)(x+y)

(m - 3n)^2 - (2a - b)^2 = (m - 3n - 2a + b)(m -
3n + 2a - b)

Therefore, the equivalent
product of the given expression is: (m - 3n)^2 - (2a - b)^2 = (m - 3n - 2a + b)(m - 3n +
2a - b).