Question

factorize it (a-b)² -5(a-b) +6 ​

Answer 1

(a - b - 2)(a - b - 3)

Step-by-step explanation:

To factorise

(a - b)² - 5(a - b) + 6

Solution:-

Let a - b = x

Therefore, the equation will be,

→ x² - 5x + 6

Splitting the middle term,

We need two coefficient of x such that their product should be 6 and sum should be -5.

Numbers are -2 and -3.

→ x² - 2x - 3x + 6

→ x(x - 2) - 3(x - 2)

→ (x - 2)(x - 3)

Substituting a - b = x, we get,

(a - b - 2)(a - b - 3)

Hence, Factorized.

Answer 2

Solution-
(a-b)^2-5(a-b)+6
We will take a-b as p to simplify this equation
So,
p2-5p+6
Now we will do middle-term splitting
Now,
p2-3p-2p+6
p(p-3)-2(p-3)
(p-3) (p-2)
Final Answer-
(a-b-3) (a-b-2)