Question

Factorize:(a-b)^2-5(a-b)+6

Answer 1

Answer:

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

Step-by-step explanation:

Given-----> ( a - b )² - 5 ( a - b ) + 6

To find ------> Factors of given expression

Solution-------> ATQ,

( a - b )² - 5 ( a - b ) + 6

Let, ( a - b ) = p

Now , putting ( a - b ) = p , in given expression .

=> p² - 5p + 6

Now , we factorise it by splitting the middle term , so we find prime factors of 6 , which is 2 and 3 and sum of these factors is 5 .

=> p² - ( 3 + 2 ) p + 6

=> p² - 3p - 2p + 6

=> p ( p - 3 ) - 2 ( p - 3 )

=> ( p - 3 ) ( p - 2 )

Putting p = a - b , we get,

=> ( a - b - 3 ) ( a - b - 2 )

Answer 2

Refer to the attached image ☺️