Expressions: guideline. Collecting like terms

There are some rules you can follow when you write an expression in algebra. These are not strict rules, but are GUIDELINES to make the work easier.

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1. Write products without multiplication sign.
Example: $2\times n\ \rightarrow\ 2n$ ;  $a\times a\ \rightarrow\ a^2$  
2. Write the number before the letter.
Example:  $x3\ \rightarrow\ 3x$  

Question: Use the guideline to rewrite the following expressions.
 $8\times m$  and  $y\times7$  

• 8m; 7y

• m8; y7

• m8; 7y

• 8m; y7

3. Write terms with letters before number terms.
Example: $4+3x\ \rightarrow\ 3x+4$   
4. Write terms in alphabetic order.
Example:  $4y\ +2x\ \rightarrow\ 2x+4y$  

Question: Use the guideline to rewrite the following expressions.
 $5+7y$  and  $7b+3a$  

• 5 + 7y;  3a + 7b

• 7y + 5;  7b + 3a

• 7y + 5;  3a + 7b

• 5 + 7y;  7b + 3a

5. When a term has more than one letter, write them in alphabetic order.
Example: $6mcax\ \rightarrow\ 6acmx$   

Question: Use the guideline to rewrite the following expression.
 $9\times g\times b\times z\times a$ 

• 9abzg

• 9abgz

• 9bagz

• 9gbza

6. Don't write negative term as the first term, even if it is in alphabetic order (Unless all the terms are negative).
Example 1: $-4a\ +\ 5b\ \rightarrow5b-4a$   
Example 2:  $-8y\ -\ 3x\ -2z\ \ \rightarrow\ \ -3x\ -8y\ -2z$  
Question: Use the guideline to rewrite the following expression.
 $-12a\ +7s\ +3-5t$ 

• 7s -12a + 3 - 5t

• 7s + 3 -12a - 5t

• -12a + 7s - 5t + 3

• 7s - 12a - 5t + 3

COLLECTING LIKE TERMS.
You can add together terms that contain the same letters.
(If there is no like terms, just rewrite the expression)
Example 1:  $2bac\ +\ 3abc\ +4cba\ \rightarrow\ 9abc$  
Example 2: $-3a\ +\ 8a\ -\ 14\ +b\ \rightarrow5a+b-14$   
Question: Use the guideline to rewrite the following expression.
 $2a-3b+7a+4$ 

• 12ab + 4

• 10a - 3b + 4

• 9a - 3b + 4

• 9a + 4 - 3b

We have finished guidelines.

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Use the guideline to rewrite the following expression. $6\times b\times a\ +\ 4a\ -\ 5\ -5b$  

• 6ab + 4a - 5 - 5b

• 6ab + 4a - 5b - 5

• 4a - 5 + 6ab - 5b

• 4a - 5b - 5 + 6ab

Use the guideline to rewrite the following expression. $-4sad-7redyn$  

• - 4ads - 7denry

• - 4sad - 7denry

• - 7denry - 4ads

• - 7denry - 4sad

Use the guideline to rewrite the following expression. $12\times t\times o\times l\times s\ -\ 4\times l\times i\times m\times f$  

• 12tols - 4lifm

• -4film + 12lost

• 12lost - 4film

• 4film - 12lost