Answer:
[tex](2h-3k)(m-n)[/tex]
Step-by-step explanation:
So we start with:
[tex]2mh-2nh-3mk+3nk[/tex]
To make this look more managable, lets seperate this into two binomials. Lets start with:
[tex]2mh-2nh[/tex]
So how can we factor this? Lets look at what both the values have in common.
We immediatly see that they both have a coefficent of 2.
They also both have a h.
This means we can factor out a 2h from both and get:
[tex]2h(m-n)[/tex]
Now lets move onto the other binomial we had:
[tex]-3mk+3nk[/tex]
Again, we can immediatly see that both values in this binomial have a 3.
Be careful however, make sure to factor out a -3, not a 3.
Another thing the two values have in common is a k.
This means we can factor out -3k to get:
[tex]-3k(m-n)[/tex]
Now lets reintroduce our first factored binomial back into this equation:
[tex]2h(m-n)-3k(m-n)[/tex]
Notice that both factored binomials have (m-n)
Because of this we can neaten up our equation into:
[tex](2h-3k)(m-n)[/tex]
How does this work?
Recall that the -3k will distrubute, or in otherwords multiply the (m-n) as [tex]3k(m-n)[/tex]. It works the same way in this form as well, since when you use foil, you multiply 2h by both m and -n, and -3k by m and -n.
And we see, if we multiply the binomials out again, we get:
[tex](2h-3k)(m-n) = 2mh-2nh-3mk+3nk[/tex]
So our answer is:
[tex](2h-3k)(m-n)[/tex]
Hope this helps! :3
