Mathematics, 19.10.2021 02:30 demarpratt1270

Factorise n2-mn

the 2 is supposed to mean squared

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Answer from: superfly903

n(n-m)

Step-by-step explanation:

We are given the quadratic expression:-

$\displaystyle \large{ {n}^{2} - mn}$

To factor this expression, do you notice that there are two n's in the expression? Yes, since in the expression, the whole terms have n-term; what we are going to do is to common factor n out!

So how do we do that? Simple, just pull n out.

$\displaystyle \large{n( {n} - m)}$

From above, you might be wondering how does it turn out like this. Do not worry, I've got you!

When we pull n out of the expression, we just divide the expression by n.

Don't get it? Let me show you!

Step 1 - Form the expression:

$\displaystyle \large{ {n}^{2} - mn}$

Step 2 - Pull n out and bracket the expression.

$\displaystyle \large{n( {n}^{2} - mn)}$

Step 3 - Divide the expression by n.

$\displaystyle \large{n( \frac{ {n}^{2} - mn}{n})} \\ \displaystyle \large{n( n - m)}$

Still not get it? Well, let's demonstrate another method.

Let's say we have the expression again!

$\displaystyle \large{ {n}^{2} - mn}$

Since n^2 comes from n•n.

$\displaystyle \large{ n \cdot n - mn}$

Bracket the expression:

$\displaystyle \large{ (n \cdot n - mn)}$

Now let's imagine that these two brackets are the doors.

m-term: There are so many of you in this bracket house! If this keeps continuing, this bracket house might be collapsed!

3 n-terms were shocked! They had to find the ways to protect their bracket house, the legacy that their cases parents gave.

But then the 2 n-terms did an unexpected! They decided to help them by going outside of the bracket house and stand there!

m-term: Why there is only one n-term outside when two of them left?

another n-term: Well, the another n-term finds food for themselves and the another one there guards our bracket house.

The End!

As we get:

$\displaystyle \large{n ( n - m)}$

Not clearing all your doubts? Let me know or ask your doubts under my comment!

Answer from: Quest

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18

Answer from: Quest

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that runner b is moving at a slower rate."

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