# Simplifying Expressions like $(a - b)(c + d - e)$

To practice with simpler Distributive Law problems, check out: Simplifying Expressions like $\,-a(3b-2c-d)$

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 $\, -cd + ce\,$).