Now we're ready to look at several extensions of the distributive law.
Recall that the ‘basic model’ of the distributive law is:
for all real numbers
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$\,a\,$, $\,b\,$, and $\,c\,$,
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$\,a(b+c) = ab + ac\,$.
There may be more than two terms in the parentheses:
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$a(b + c + d) = ab + ac + ad$
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$a(b + c + d + e) = ab + ac + ad + ae$
and so on.
All the usual rules for dealing with signed terms hold.
For example,
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$-a(2b + c + 4d + f) = -2ab - ac - 4ad - af$
Remember to determine the sign (plus or minus) first,
the numerical part next,
and the variable part last.
EXAMPLE:
Question:
Simplify:
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$\,a(b - c + e)$
Answer:
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$ab - ac + ae$
Do not change the order of the letters:
write
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$\,ab-ac+ae\,$, not (say) $\,ba-ac+ea\,$.
Even though answers like ‘$\,ba-ac+ea\,$’ are correct,
they are not recognized as correct by this program.
Master the ideas from this section
by practicing the exercise at the bottom of this page.
When you're done practicing, move on to:
Basic FOIL
In each term, variables must be written in the order they appear, from left-to-right, in the original expression.