SIMPLIFYING EXPRESSIONS LIKE $\,-a(3b-2c-d)$
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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 $\,a\,$, $\,b\,$, and $\,c\,$, $\,a(b+c) = ab + ac\,$.

There may be more than two terms in the parentheses:

$a(b + c + d) = ab + ac + ad$
$a(b + c + d + e) = ab + ac + ad + ae$
and so on.

All the usual rules for dealing with signed terms hold.
For example,

$-a(2b + c + 4d + f) = -2ab - ac - 4ad - af$
Remember to determine the sign (plus or minus) first,
the numerical part next,
and the variable part last.

EXAMPLE:
Question: Simplify: $\,a(b - c + e)$
Answer: $ab - ac + ae$
Do not change the order of the letters:
write $\,ab-ac+ae\,$,   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