chenellelewis6
Answered

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factorize 2mh-2nh-3mk+3nk ​

Sagot :

clarch19

Answer:

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

Step-by-step explanation:

factor by grouping, you can group the first two terms and the last two terms:

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

there will be one factor in common, use that factor in combination with the factors that are not duplicated:

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

bowmaian000

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

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