1. Expressions

2. LLike terms are those that have EXACTLY matching variables (order does not matter) YYou can add and subtract the coefficients to like terms by using the distributive property in reverse TThe Distributive Property: a(b + c) = ab + ac and (b + c)a = ab + ac FFor example: 3x + 5x = (3 + 5)x = 8x EEx1. Simplify: 3a + 2b – 8a + b EEx2. Simplify

3. EEx3. Simplify IIf it helps, you can change subtraction signs to adding negative values EEx4. Simplify 10x – 8y – 4x – (-2y) IIf there is a negative or subtraction sign directly outside a set of parentheses containing either a sum or difference, distribute the sign to each term within the parentheses EEx5. Simplify 10x – (5x + 8) + 12 – 3x EEx6. Simplify (5n – 8p) – (9n – 5p) + 4p

4.  Opposite of a Sum Property: For all real numbers a and b, -(a + b) = -a + -b = -a – b  Opposite of Opposites Property (Op-op property): For a real number a, -(-a) = a  Opposite of a Difference Property: For all real numbers a and b, -(a – b) = -a + b  Ex7. Simplify  Ex8. Simplify  Sections from the book to read: 3-6 and 4-5

5. AA rational expression contains at least one fraction YYou must have a common denominator in order to add or subtract fractions MMultiply the numerator and denominator of the fraction by the same number ◦D◦Do this to both fractions so that the denominators are the same TThen add or subtract the numerators (combining like terms) and leave the denominator the same

6. SSimplify each rational expression EEx1. EEx2. EEx3. EEx4. SSections of the book to read: 3-9, 4-5, and 5-9

7.  When you are multiplying terms, add the exponents of the variables that are alike  Product of Powers Property: For all m and n, and all nonzero b,  Simplify  Ex1.  Ex2.  Ex3.

8. WWhen you raise a power to a power, multiply the exponents PPower of a Power Property: For all m and n, and all nonzero b, EEx4. Simplify IIf the exponent is directly outside of parentheses that contain a monomial, then you multiply every exponent inside of parentheses by the one outside PPower of a Product Property: For all nonzero a and b, and for all n,

9. SSimplify EEx5. EEx6. EEx7. Solve for n. SSections from the book to read: 2-5, 8-5, 8-8 and 8-9

10.  A negative exponent does NOT make anything in the expression negative  Negative Exponent Property: For any nonzero b and all n, the reciprocal of  Only the power with the negative exponent is changed, it is moved to the other half of the fraction  Write with no negative exponents  Ex1.Ex2.Ex3.  Ex4. Write as a simple fraction

11.  Ex5. Write as a negative power of an integer  Zero Exponent Property: If g is any nonzero real number then,  Ex6. Write without negative exponents  Ex7. Simplify  Ex8. Simplify  Sections from the book to read: 8-2, 8-6, 8-9, and 12-7

12.  When dividing monomials, subtract the exponents of the matching variables  Quotient of Powers Property: For all m and n, and all nonzero b,  Write answers without negative exponents unless the directions allow it  Ex1. Simplify  Write as a simple fraction ◦ Ex2. Ex3.

13.  Simplify. Write as a fraction with no negative exponents ◦ Ex4. Ex5.  Power of a Quotient Property: For all nonzero a and b, and for all n,  Write as a simple fraction with no negative exponents ◦ Ex6.Ex7.Ex8.  Sections from the book to read: 8-7, 8-8, 8-9

14.  To multiply rational expressions, multiply the numerators together and the denominators together and be sure to simplify ◦ You can simplify before you multiply or after  To divide rational expressions, flip the second expression and then multiply  Do NOT use mixed numbers with variables ◦ Yes: or No:

15.  Simplify. Write the answer with no negative exponents.  Ex1.Ex2.  Ex3.Ex4.  Sections of the book to read: 2-3 and 2-5

16.  Multiplying a monomial by a polynomial is using the distributive property  Write your answers in standard form  A subscript is NOT a mathematical process, it is just another name for a variable ◦ i.e. x 1 and x 2 are two different variables  Multiply ◦ Ex1. ◦ Ex2.

17.  If you are multiplying a binomial by another binomial, FOIL will help make sure you don’t miss any terms  FOIL: First, Inner, Outer, Last ◦ Multiply the First term in each binomial, then multiply the two Inner terms, then multiply the two Outer terms, then multiply the two Last terms, and finally combine like terms  Multiply ◦ Ex3. (x + 4)(x + 6)Ex4. (m – 3)(m – 5) ◦ Ex5. (n + 6)(n – 9) Ex6. (2a + 3)(a – 5) ◦ Ex7. (3w² + 5)(2w² ─ 7)  Sections of the book to read: 3-7, 10-1, 10-3, and 10-5

18. UUse the Extended Distributive Property in order to multiply polynomials ◦M◦Multiply every term in the first polynomial by every term in the second polynomial SSee page 633 for a rectangular way to demonstrate this property YYou can write the work vertically or horizontally (your choice) MMultiply ◦E◦Ex1. ◦E◦Ex2.  Sections of the book to read: 2-1 and 10-4

19. PPerfect Square Patterns: For all numbers a and b (a + b)² = a² + 2ab + b² and (a – b)² = a² - 2ab + b² ◦Y◦You can use this shortcut when multiplying SSquare of a sum is a sum squared ◦i◦i.e. (a + b)² SSquare of a difference is a difference squared ◦i◦i.e. (a – b)² TThe result of a square of a sum and a square of a difference is called a perfect square trinomial EExpand ◦E◦Ex1. (x – 5)² Ex2. (a + 7)² Ex3. (4m – 3)²

20. IIf you multiply two binomials that are identical except one is addition and one is subtraction, the outer and inner terms will cancel out ◦T◦The result is called the difference of squares DDifference of Two Squares Pattern: For all numbers a and b, (a + b)(a – b) = a² - b² EExpand ◦E◦Ex4. (x + 5)(x – 5)Ex5. (3x – 2)(3x + 2) YYou can use these patterns to do some basic arithmetic EEx6. 43²Ex7. 81 · 79 SSection of the book to read: 10-6

21. OOnce you read the word “is,” that is where you put the equal sign IIf the book uses the word “the quantity,” that is where you put the parentheses WWrite an expression for each sentence ◦E◦Ex1. The sum of 8 and the product of a number and 6 ◦E◦Ex2. The quantity of a number plus seven will then be divided by 9 ◦E◦Ex3. The difference of a 7 and a number WWhen given a table, look for a pattern to describe the situation

22. EEx4. Write an equation based on the information EEx5. Pencils sell for $0.24 each while notebooks sell for $0.72 each. Write an expression to describe how to find the total cost if you buy p pencils and n notebooks EEx6. A parking lot charges $3 for the first hour and then $2 for every hour after that ◦A◦A) If a car is in the lot for 6 hours, how much will the owner pay? ◦B◦B) If a car is in the lot for h hours, how much will the owner pay? SSections of the book to read: 1-7, 1-9, and 3-8 x1346810 y51114202632