Question

Help?? Factor.
ab + 6b − 5a − 30

Answer 1

\(\large\rm ab+6b-5a-30\)

Answer 2

i know the next part is (6b +ab) + (-30-5a) but why are the switches areound?

Answer 3

So you chose to group things like this,\[\large\rm (ab+6b)+(-5a-30)\]And then switch the second pieces?\[\large\rm (ab+6b)+(-30-5a)\]And you're confused why they're allowed to switch like that in the second brackets?
Or you wondering why we would want to even do that?

Answer 4

yes both questions!

Answer 5

The `why` doesn't become apparent until you start factoring.
So don't worry about that. :)
Just skip that step and jump right into the factoring.

Answer 6

But the reason we're `allowed to do this` is because uhhh\[\large\rm -30-5a\quad=(-30)+(-5a)\]Rewrite your subtraction as addition between two negative numbers,
from there you can simply switch them because it's addition, ya?\[\large\rm =(-5a)+(-30)\]And then dropping all the bracket nonsense,\[\large\rm -5a-30\]

Answer 7

But honestly, you shouldn't worry about switching them right away.
Factor first.\[\large\rm (ab+6b)+(-5a-30)\]The terms in the first brackets have what in common? Looks like the b, ya?

Answer 8

yes

Answer 9

so what do i do now?

Answer 10

So we'll pull the b out from each term in the first brackets,\[\large\rm b(a+6)+(-5a-30)\]That step make sense? :o
How bout the other brackets?
What do -5a and -30 share in common?

Answer 11

yes! um multiples

Answer 12

right?

Answer 13

what? :3

Answer 14

common multiples

Answer 15

Yes. And you'll have to break down the -30 to see what they share in common. The -5a is already as simple as possible.

Answer 16

5 x -6

Answer 17

-5 x 6

Answer 18

b(a + 6) -5(a + 6)

Answer 19

Mmm ok good!

Answer 20

Understand the next step? :O

Answer 21

there's a next step? what do we do?

Answer 22

@zepdrix ?

Answer 23

Well notice what we've ended up with,\[\large\rm b\color{orangered}{(a + 6)} -5\color{orangered}{(a + 6)}\]both of these terms, between the subtraction, have something in common, ya?

Answer 24

So we'll need to factor further.

Answer 25

ohhhhhh (b-5)(a+6)

Answer 26

\[\large\rm [b\color{orangered}{(a + 6)} -5\color{orangered}{(a + 6)}]\quad=\quad[b-5]\color{orangered}{(a + 6)}\]Good good good.

Answer 27

So there is our answer.
Yayyy team! We did it!

Answer 28

lol yay! :)

Answer 29

Factoring is not too bad :O
Just practice practice practice