Question

Factorize the following
2mh+3mk-2nh-3nk​

Answer 1

(2h + 3k) (m - n)

Explanation:

factor by pairing: pair and factor the first two terms, then pair and factor the remaining two; there should be one factor which duplicates

m is common factor of 1st pair: m(2h+3k)

n is common factor of 2nd pair: n(2h+3k)

answer is one of the duplicate factors (2h+3k) times terms not contained in parentheses (m+n)

Answer 2

`(2h+3k)(m-n)`

Explanation:

`2mh+3mk-2nh-3nk`

Just look at the common terms

`2mh-2nh-3nk+3mk = 2h(m-n)-3k(n-m) = 2h(m-n)+3k(m-n)`

By grouping we have

`2h(m-n)+3k(m-n) =\boxed{(2h+3k)(m-n)}`