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One method commonly taught is called FOIL. It means that for problems involving 4 terms that
are in two sets of parentheses such as these, multiply the FIRST terms in each set of
parentheses.
Next multiply the OUTSIDE terms of the four terms and add the result to the product of
the first terms.
Then multiply the INSIDE terms of the four terms and add the result to the previous answers.
Finally, multiply the LAST terms in each set of parentheses and add that result to the previous
answers.
Let's work the problem:
Multiply the FIRST terms (the F in FOIL). In each set of parentheses for this problem
the first term is x. So multiply x times x to get .
Next multiply the OUTSIDE terms (the O in FOIL). The outside terms of the four terms
is x from the first set of parentheses and +9 from the second set of parentheses.
The product of these two terms is +9x. Add this to the previous answer and you
now have
Then multiply the two INSIDE terms (the I in FOIL) of the four terms. The inside terms
are the two middle terms of the four terms. These are: -10 from the first set of parentheses
and +x from the second set of parentheses. The product of these two terms is -10x.
Add this to the previous answer and you have .
Finally, multiply the LAST terms in each set of parentheses (the L in FOIL). The last term
in the first set of parentheses is -10 and the last term in the second set of parentheses
is +9. Multiplying these two results in -90. Add this to the previous result to get .
Notice in the answer that the terms + 9x - 10x can be added to get -x. When you do that,
the answer simplifies to the final answer of:
Hope this helps you to understand problems of this form. Just FOIL them!
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