SIMPLIFYING EXPRESSIONS LIKE $\,(a - b)(c + d - e)\,$
EXAMPLES:
Simplify: [beautiful math coming... please be patient] $(a - b)(c + d - e)$
Answer: [beautiful math coming... please be patient] $ac + ad - ae - bc - bd + be$
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 [beautiful math coming... please be patient] $\,ac + ad - ae\,$).
Then, multiply the second term in the first group by everything in the second group (giving [beautiful math coming... please be patient] $\,-bc - bd + be\,$).
Do not change the order of the letters!
Write the letters in the order that they occur, going from left to right.
Simplify: [beautiful math coming... please be patient] $(a - b + c)(-d + e) $
Answer: [beautiful math coming... please be patient] $-ad + ae + bd - be - cd + ce$
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 [beautiful math coming... please be patient] $\,-ad + ae\,$).
Then, multiply the second term in the first group by everything in the second group (giving [beautiful math coming... please be patient] $\,bd - be\,$).
Finally, multiply the third term in the first group by everything in the second group (giving [beautiful math coming... please be patient] $\, -cd + ce\,$).
Master the ideas from this section
by practicing the exercise at the bottom of this page.

When you're done practicing, move on to:
Practice With the Mathematical Words
‘and’, ‘or’, ‘is equivalent to’

 
 
Simplify: