You can
put this solution on YOUR website!Given:
.
.
First look at the numbers that multiply each of the terms to see if there is are common
factors. The first term is multiplied by 1 (understood), the second term by -4, and the
third term by -21. These three numbers have no common factors, so we don't change them.
.
Next look at the x part of each of the terms. The first term contains
, the second
term
, and the third term
.
is common to each term because
and
. So we can pull an
from each term and
we get:
.
Next notice that you have a "y" common to all terms. So pull a y out as a multiplier and
you have:
.
.
Notice that we can multiply out
and the result should be
the original given expression. This is just a "check".
.
So we are down to
. We now need to see if we can factor the
Yes we can. It might be a little easier to see if we wrote
in an equivalent form of
to change the expression to:
.
and we might see it a little more clearly if we let xy = A to get:
.
.
We can try to factor this into (A + ___)*(A + ___). The underscores have to be two numbers
that are factors of -21. These numbers could be 21 and 1 or 7 and 3. With their appropriate signs
they must sum to -4. -7 and + 3 do that. If they are multiplied they give -21 and if they are
added they give -4 which is the multiplier of the center term that contains just A.
.
So we can write that
factors to
. But also recall
that we said A was equal to xy. So now we can substitute xy into the two factors and get:
.
.
And so we can say that
factors to
and we can
carry this result back into this equation that we got earlier:
.
.
In this equation, replace
with
and the result is:
.
.
and that's the answer to your problem.
.
I know this is confusing, but I hope that you can see your way through it. If you can
understand all the maneuvering in this you will have made a lot of progress.
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