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

by Dr. Carol JVF Burns (website creator)
Follow along with the highlighted text while you listen!

Here, you will get some higher-level practice with the distributive law.

EXAMPLES:
Simplify: $(a - b)(c + d - e)$
Answer: $ac + ad - ae - bc - bd + be$
Note:   You must write the terms in the order indicated in this example.
Other orders are correct, but are not recognized as correct by this web exercise.
Start by multiplying the first term in the first group by everything in the second group (giving $\,ac + ad - ae\,$).
Then, multiply the second term in the first group by everything in the second group (giving $\,-bc - bd + be\,$).
Do not change the order of the letters!
Write the letters in the order that they occur, going from left to right.
Simplify: $(a - b + c)(-d + e)$
Answer: $-ad + ae + bd - be - cd + ce$
Note:   You must write the terms in the order indicated in this example.
Start by multiplying the first term in the first group by everything in the second group (giving $\,-ad + ae\,$).
Then, multiply the second term in the first group by everything in the second group (giving $\,bd - be\,$).
Finally, multiply the third term in the first group by everything in the second group (giving $\, -cd + ce\,$).
Master the ideas from this section

When you're done practicing, move on to:
Dividing More Than One Term by a Single Term

Simplify:

CONCEPT QUESTIONS EXERCISE: