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slava [35]
2 years ago
12

Factorize 2mh-2nh-3mk+3nk ​

Mathematics
2 answers:
Nookie1986 [14]2 years ago
8 0

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)

nika2105 [10]2 years ago
5 0

Answer:

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

Step-by-step explanation:

So we start with:

2mh-2nh-3mk+3nk

To make this look more managable, lets seperate this into two binomials. Lets start with:

2mh-2nh

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:

2h(m-n)

Now lets move onto the other binomial we had:

-3mk+3nk

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:
-3k(m-n)

Now lets reintroduce our first factored binomial back into this equation:

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

Notice that both factored binomials have (m-n)

Because of this we can neaten up our equation into:

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

How does this work?

Recall that the -3k will distrubute, or in otherwords multiply the (m-n) as 3k(m-n). 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:

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

So our answer is:

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

Hope this helps! :3

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Answer:

x = 1 or x = -1

Step-by-step explanation:

Given equation:

x^{100}-4^x \cdot x^{98}-x^2+4^x=0

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Divide both sides by -1:

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Factor the first two terms and the last two terms separately:

\implies 4^x(x^{98}-1)-x^2(x^{98}-1)=0

Factor out the common term (x^{98}-1) :

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Using the <u>Zero Product Property</u>, set each factor equal to zero and solve for x (if possible):

\begin{aligned}x^{98}-1 & = 0 & \quad \textsf{or} \quad \quad4^x-x^2 & = 0 \\x^{98} & =1 & 4^x & = x^2 \\x & = 1, -1 & \textsf{no}& \textsf{ solutions for } x \in \mathbb{R}\end{aligned}

Therefore, the solutions to the given equation are: x = 1 or x = -1

Learn more here:

brainly.com/question/27751281

brainly.com/question/21186424

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According to the scale, we can simply multiply the distance that Sonja measured on the map by the actual mile distance that it states on the scale (1/2 or 0.5) to calculate the actual distance between Sonja's house and Sal's house like so...

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