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21x^2-49x+6xy-14yHow do you factor by grouping?

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1 Answer

Let's group it like this

(21x2 - 49x) + (6xy - 14y)

Notice that we can factor out 7x from the first part and 2y from the second part to get

7x(3x - 7) + 2y(3x - 7)

notice that there is a common factor 3x - 7.

We can factor it out of the whole expresssion to get

(7x + 2y)(3x - 7)



If you want a generic step-by-step for any problem where you need to factor by grouping, here you go.

(1) Look at the equation for "pairs" that have something in common, especially variables (e.g. x, y, z, etc.)

(2) Group the pairs with parentheses.

(3) Factor out what you can for each pair.

(4) You should be left with a common factor.  Factor that out of the whole expression.

(5) In the end you should be left with something like this: (a + b)(c + d).  The (a + b) term are the two parts you pulled out in step (3) and the (c + d) term is the common factor you were left with in step (4)