﻿ Simplifying Expressions like -a(3b - 2c - d)
SIMPLIFYING EXPRESSIONS LIKE $\,-a(3b-2c-d)$

by Dr. Carol JVF Burns (website creator)
Follow along with the highlighted text while you listen!
• PRACTICE (online exercises and printable worksheets)
Want more details, more exercises?

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