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Undoing the Distributive Property

Altogether, we'll factor out a 2x (y^2)

2 (x^2) (y^5) - 4x (y^3) + 6 (x^4) (y^2) = 2x (y^2) ( _ ) ... we need to figure out what goes inside the parentheses

Think backwards -- and always keep distributing in mind.

Look at the first term:

We took  2x (y^2)out of 2 (x^2) (y^5)

What would be left?

Or...

What would we need to multiply2x (y^2)by to get
back up to2 (x^2) (y^5)  ?
We need anotherx... and ay^3...

2 (x^2) (y^5) - 4x (y^3) + 6 (x^4) (y^2) = 2x (y^2) ( x (y^3) ____ ) ... check by distributing

Now, the second term:

We took2x (y^2)out of -4x (y^3)

So, we need a -2... and a y...

2 (x^2) (y^5) - 4x (y^3) + 6 (x^4) (y^2) = 2x (y^2) (x (y^3) -2y ____ )

Check it!