Factorise the folowing:$3(x+y)^2-5(x+y) +2$

Given:

The given expression is $3(x+y)^2-5(x+y) +2$

To do :

We have to factories the given expression.

Solution :

Let $(x+y) = k$

Therefore,

$3(x+y)^2-5(x+y) +2 = 3k^2-5k+2$

We have to factorize $3k^2-5k+2$

$3k^2-5k+2 = 3k^2-3k-2k+2$

                   $=3k(k-1)-2(k-1)$

                   $= (3k-2)(k-2)$

Therefore,

$3(x+y)^2-5(x+y) +2 = (3(x+y))((x+y)-2) = 3(x+y)(x+y-2)$

The factors of $3(x+y)^2-5(x+y) +2$ are $3, (x+y), (x+y-2)$

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Updated on: 10-Oct-2022

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