Need some help on this please?

Question

Factor this expression.

Could someone show me step by step how to achieve the right answer. I am trying to practice and get a hang of this

(a - b)r - (a - b)s

Thanks

Answer 1

(a-b)r - (a-b)s

Think of a-b as c
cr-cs
=c(r-s)

Therefore
(a-b)r -(a-b)s
=(a-b)(r-s)

Answer 2

Unfortunately, I don't know how to show you the answer step-by-step, but I'll try to explain it.

(a - b)r - (a - b)s
(a - b)(r - s)

Essentially, when your factoring, you're goal is to try to simplify the main term by pulling out values or variables that can be found in each term. If you think about it, it is almost the same thing as dividing each term by that value, but instead you pull it out to one side. You can check your factoring by re-distributing the value through and making sure you get your original expression.

If you look at more simple example like: ar - as, you can see that both terms share the common variable of a. Instead of multiplying that value to both terms individually, and alternate way to write it would be: a(r - s). By looking at your original problem, you can see that the concept is exactly the same, except that instead of just a variable a on its own, the quantity (a - b) is the one being multiplied through.

It's hard to show steps with factoring problems like these because you pretty much just work them through in your head, and with practice you can see the patterns and get the answers, but I hope my explanation helps.

Answer 3

First let's do a simple example in the form of the one you posed.

Example

xr -xs

Now we factor by factoring the x out of the expression.

x(r-s)

Simple, right?

Now we do the same thing to your expression:
(a - b)r - (a - b)s

Here we factor out (a-b)

So we have

(a-b)(r-s)

OK?

Answer 4

to factorise an expression, you have to pick out like terms. initially, the expression was
ar-br-as+bs
the like term in ar and br is r (they both contain r)
so, r is picked out and they are both divided by r
so, it becomes
r(a-b)
in order to be able to factorise the expression,
we must also have (a-b) in the second part of the equation
in order to get this, the like term must be -s
therefore the equation becomes
(a-b)r-(a-b)s
collect like terms between them again (a-b)
the expression becomes
(a-b)(r-s)