Thread: Common Factors

1. Common Factors

Factor by grouping

xy + 12 + 4x + 3y = (x+3)(4+y)<-------txtbk ans

x² + x - xy - y = (x+1)(x-y)<--------txtbk ans

Please help. I'm confused how to arrive to the answer. Can someone show me the steps? Thank you!

2. $xy + 12 + 4x + 3y$

$xy + 3y + 4x+ 12$

$y(x + 3) + 4(x+ 3)$

$(x + 3)(y+4)$

Do you follow?

3. Originally Posted by pickslides
$xy + 12 + 4x + 3y$

$xy + 3y + 4x+ 12$

$y(x + 3) + 4(x+ 3)$

$(x + 3)(y+4)$

Do you follow?
Do you always have to rearrange the expression before solving?

Can't it also say x(y+4)+3(4+y) in the 3rd step?

And how would you know to group which ones together?

4. Originally Posted by larry21
Do you always have to rearrange the expression before solving?
Only so you can take out a common factor.

Originally Posted by larry21
Can't it also say x(y+4)+3(4+y) in the 3rd step?
Yep, addition commutes.

Originally Posted by larry21

And how would you know to group which ones together?
You try to find groups where there is a common factor that once taken out gives the same inside each bracket. Sometimes might take a little trial and error. Perseverance will be your friend.