### Chapter 5: Algebra... Different "Faces" of Algebra (I)

Write an algebraic expression that has 3 terms involving variables p and q.

Based on what's posted in the comments:
(i) The following are algebraic expressions comprising of 3 terms involving variables p and q:
• 4p+4q+4pq
• 3q + 6p - 5p
• 100p+p x 300q-q
• px2+p^2-pq
• 111p+11q-10px3
(ii) The following are algebraic expressions with less than 3 terms involving p and q:
•  p+q
•  p-q
• p×2p+pq
• 5px2p-q
• 4p x 2q^2 - 2p^2
• (p+p)/3qx2p
• p^2 x q^5 - pq
• (p+q)*2p/3q
• p^5 x q^9 - p
• p^10 x q^2 - pq
• 162p + 8p/2q x 83q
• pxq
• p^2*3q÷pq
• [99p+(-200000q)]^86pq
(iii) The following are NOT algebraic expression:
• 7p*2q+8q=10p+2p*q
Can you figure out what distinguishes (i), (ii) and (iii)?

1. This comment has been removed by the author.

2. Mark :) :( :'( (^^^) :D :O :42: O:) :p 3:)4/20/2011 11:08:00 AM

4p x 2q^2 - 2p^2

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4. [99p+(-200000q)]^86pq

5. Chan Shawn Kit4/20/2011 11:45:00 AM

1)p+q
2)p-q
3)pxq

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7. 1) (p+p)/3qx2p

The previous comment has been DELETED

8. 100p+p x 300q-q

9. (p+q)*2p/3q

10. 7p*2q+8q=10p+2p*q

11. 3q + 6p - 5p

12. p^2 x q^5 - pq

13. p^5 x q^9 - p

-Owen

14. p^10 x q^2 -pq

15. 5px2p-q

16. 111p+11q-10px3

17. 162p + 8p/2q x 83q

18. 7p^3+9q+1q

19. pq^2+p

20. Mark :) :( :'( (^^^) :D :O :42: O:) :p 3:)4/21/2011 08:12:00 AM

When there are 3 or more terms, they are all completely different, and when it says "3 terms", it refers to something like pq^2 + 2p ÷ 3q, where the terms are pq^2, p, and q, and not like 2p + p + 3p, where the only term is p.

21. 4p x 2q^2 - 2p^2

22. p*p+2q - q

23. Q : Can you figure out what distinguishes (i), (ii) and (iii)?

The signs '+' , '-' , 'x' , ' /' and ' =' that is placed in the expression to group the terms in the expression distinguish (i), (ii) and (iii)?

The terms in the expressions is separated by '+' and '-' signs.
Eg : 2p + q- p*3

The last term , p*3 , is counted as a term as it is solve together so the multiply sign does not distinguish the 'p' and the '3' as two terms

The multiply and divide signs between the terms groups the terms as one.

Eg : p*4+ q*5 + 4pq

There is three terms in this expression but not five terms.The two terms are p*4 and q*5 are solve together.

In ' iii' , it is a equation instead of a expression because of a equal sign.