Question

Factorise 3(x+y)^2-5 (x+y)+2​

Answer 1

Answer:

Consider, 3(x + y)2 – 5(x + y) + 2

= 3(x + y)2 – 3(x + y) – 2(x + y) + 2

= 3(x + y)[(x + y) – 1] – 2[(x + y) – 1]

= [(x + y) – 1][3(x + y) – 2]

= [x + y – 1][3x + 3y – 2]

Answer 2

Given,

The expression, 3(x+y)²-5(x+y)+2.

To find,

The factors of the given expression.

Solution,

The factors of 3(x+y)²-5(x+y)+2 will be (x+y-1) (3x+3y-2).

We can easily solve this problem by following the given steps.

Now, we can factorise this expression by splitting its middle terms into two terms such that their multiplication will be 3(x+y)²×2 and their addition will be -5(x+y).

So, these two terms will be -3(x+y) and -2(x+y).

According to the question,

3(x+y)²-5(x+y)+2

3(x+y)²-3(x+y)-2(x+y)+2

Taking 3(x+y) common from the first two terms and -2 from the last two terms,

3(x+y) (x+y-1) -2(x+y-1)

Taking (x+y-1) common,

(x+y-1) [3(x+y)-2]

(x+y-1) (3x+3y-2)

Hence, the factors of 3(x+y)²-5(x+y)+2 are (x+y-1) (3x+3y-2).