1. Algebra

3. Algebra Vocabulary
Algebraic Expression- a math sentence involving a variable or unknown
Variable- a symbol for a letter we don’t know yet
Constant- a number on its own
Coefficient- a number used to multiply a variable
Operator- a symbol that shows an operation
Like Terms- are terms whose variables (and their exponents) are the same. In other words, terms that are "like" each other. (Note: the coefficients can be different)
Polynomial- an equation that has constants, variables and the exponents; NEVER DIVISION

4. Rules You can only combine like terms
Signs (+/-) are attached to the coefficient and variable
- (-) = +
Positive + Positive = Positive
Positive + Negative = the sign of the larger digit
Negative – Negative = the sign of the larger number
Negative – Positive = negative
Positive x Positive = Positive
Positive x Negative = Negative
Negative x Negative = Positive
Positive Positive = Positive
Negative Negative = Positive
Negative Positive = Negative
Positive Negative = Negative

5. Operation Key Words
Addition: sum, total, plus, in all, all together, and, increased by
Subtraction: difference, less than, fewer, from, take away, are not, remain, how many more, exceed, remain
Multiplication: times, each, in all, twice, product, factor, multiple, multiplied by
Division: same, split, equal groups, separate, shared equally, distribute, cut up

6. Take away 6 from 5 times of g
Write an expression
Identify the variable
Look for key words
Identify the operations
Example:
Take away 6 from 5 times of g
Subtract and Multiply
Answer: 5g-6

7. Write an expression 5 more than quotient of x and 3
Addition and Division
5 + x/3
9 less than 8 times of y
Subtraction and Multiplication
8y-9
Add 2 times of k and one-third
Addition and Multiplication
2 + 1k/3

8. Writing and Expression
Product of 5 and y
Quotient of 6 and a
Take away 2 from q
4 is added to p
3 times of x
One-half of q is added to 7
Two-third of the sum of 5 and m
Six-fifth of h is subtracted from 3
5 less than quotient of w and 7
9 minus h

9. Adding Polynomials Line up like terms (this may involve re-arranging)
2x2 + 3xy+4
3x2+5xy+2
Add down the columns (Add like terms)
3x2+ 5xy +2
Note: the only aspect that changes is the coefficient
Answer: 5x2+ 8xy + 6

10. Adding Polynomials

11. Adding Polynomials

12. Subtracting Polynomials
Line up like terms (this may involve re-arranging)
2x2 + 3xy+4
3x2+5xy+2
Multiply all terms in the second polynomial by -1
3x2+5xy x2- 5xy -2
Add down the columns (Add like terms)
2x2 + 3xy +4
-3x2- 5xy -2
Note: the only aspect that changes is the coefficient
Answer: -1x2-2xy + 2

13. Subtracting Polynomials

14. Subtracting Polynomials