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If $(2 a - 3 b) (m x + n y)$ is the factorization of the polynomial $2 a (x + y) - 3 b (x + y)$ then the values of ‘m’ and ‘n’ are [[1]] and [[2]] respectively.

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Detailed Solution

(2 a - 3 b) (m x + n y)

is the factorization of the polynomial

2 a (x + y) - 3 b (x + y)

then the values of ‘m’ and ‘n’ are 1 and 1 respectively.
The given polynomial is

2 a (x + y) - 3 b (x + y) .

We will take out the common term from the given polynomial to simplify it further.
Since

x + y

is common, we take it out.
We then get,

2 a (x + y) - 3 b (x + y) = (x + y) (2 a - 3 b)

On comparing

(x + y) (2 a - 3 b)

with

(2 a - 3 b) (m x + n y),

the values of ‘m’ and ‘n’ are 1 and 1 respectively.

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