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By Grouping

Something like this will pop up on you if you go on to take Calculus... Other than that, you probably won't see it anywhere.

Let's start out very simply...

Factor these:

5w + 3xw = ?

5y^2 + 3xy^2 = ?

5k^3 + 3xk^3 = ?

Now, can you do these?

5 ( blob ) + 3x ( blob ) = ?

5 ( w + 2 ) + 3x ( w + 2 ) = ?
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This type of guy will show up half way through this process... You just did the last step of factoring by grouping. Aren't you thrilled?

Here are some more last-step guys:

2w ( x + 5 ) + 7 ( x + 5 ) = ( x + 5 ) ( 2w + 7 ) ... factor the ( x + 5 ) blob out

x^2 ( y - 3 ) - 8 ( y - 3 ) = ( y - 3 ) ( x - 8 ) ... factor the ( y - 3 ) blob out