1. Expressions and Polynomial Review
August 22, 2016

2. Essential Questions
How do I identify the parts of an expression in terms of context?
How do I combine like terms?
How do I add or subtract polynomials?
How do I multiply polynomials?
How do I use polynomials to find the area or perimeter of a polygon?

3. Outline Vocabulary Review Parts of an Expression
Evaluating Expressions
Adding Polynomials
Subtracting Polynomials
Multiplying Polynomials
Perimeter
Area

4. Vocabulary Review Binomial expression Monomial expression Expression
Factor
Integer
Perimeter
Whole Number
Polynomial expression

5. Vocabulary Review Area Degree of Term Terms Coefficients
Solution of an equation
Inverse operation
Variable
Constant
Standard form of polynomial

6. Writing Expressions + (add) - (subtract) x (multiply) ✢ (divide)
When writing expressions use these words with the following operational signs
+ (add)
- (subtract)
x (multiply)
✢ (divide)
Add
Plus
The sum of
Subtract
Minus
The difference of
Times
Multiplied by
The product of
Divided by
The quotient of

7. Writing Expressions Examples include:
m + 7  The sum of m and 7. or M plus 7.
w-6  The difference of w and 6 or W minus 6.
h X 9  The product of h and 9. or H times 9.
c ✢ 8  The quotient of c and 8. or C divided by 8.

8. Writing Expressions
Example: Tim scored a total of 18 points in the football game, and he scored g points in the second half of the game. Write an expression to determine the number of points he scored in the first half of the game. Then find the number of points he scored in the first half of the game if he scored 12 points in the second half of the game.

9. Writing Expressions Scored 18 points for entire game
Scored g points in the second half
18-g = points in first half
g= 12 points in second half
18-(12) = = 6 points in first half

10. Parts of an expression
coefficient
variable

11. Parts of Expression
6abc
How many factors does this expression have?

12. Evaluating Expressions
Evaluating expressions means that you are substituting a number for your variable.
For example: g-h, where g=8 and h=5
g-h = 8-5 =3
Another example : 2a+b, where a=4 b=7
2a+b = 2(4) + 7 = 8+7 =15

13. Adding Polynomials
Add the following polynomials using column form: (4x2 – 2xy + 3y2) + (-3x2 + 2y2)
(4x2 - 2xy + 3y2) + (-3x2 + 2y2)
Line up your like terms
4x2 - 2xy + 3y2
+ -3x y2
x2 - 2xy + 5y2

14. Subtracting Polynomials
Subtract the following polynomials using column form: (4x2 + 3y2) - (-10x2 +5xy - 7y2 - 9)
(4x2 + 3y2) + (10x2 - 5xy + 7y2 + 9)
Line up your like terms
4x y2
+ 10x2 - 5xy + 7y2 + 9
14x2 -5xy + 10y2 + 9

15. Subtracting Polynomials
Subtract the following polynomials using column form: (3x2 – 2xy + 3y2) - (-6x2 +11xy - 7y2)
(3x2 - 2xy + 3y2) + (6x2 - 11xy + 7y2)
Line up your like terms
3x2 - 2xy + 3y2
+ 6x2 -11xy + 7y2
9x2 -13xy + 10y2

16. Multiplying a polynomial by a monomial
Multiply: 3x2y(2x + 4y2)
To multiply we need to distribute the 3x2y over the addition.
3x2y(2x + 4y2) = (3x2y * 2x) + (3x2y* 4y2) = 6x3y + 12x2y3

17. Multiplying a polynomial by a polynomial
(x + 3)(x – 3)
x(x) + x(–3) + 3(x) + 3(–3)
x2 – 3x + 3x – 9
x2 – 9

18. Multiplying a polynomial by a polynomial (perfect square)
(x + 7)2
(x + 7)(x + 7)
x(x) + x(7) + 7(x) + 7(7)
x2 + 7x + 7x + 49
x2 +14x +49

19. Area and Perimeter
A rectangle has a length of 2x2+3 and a width of x2. Write and simplify an expression for the perimeter and area of the rectangle.

20. Perimeter
2x2+3 x2 x2
2x2+3

21. Perimeter
Perimeter = side + side + side + side
Perimeter = 2x2+3 + x2 + 2x2+3 + x2
Perimeter = 6x2+6

22. Area
2x2+3 x2

23. Area
Area = length x width
Area = (x2)(2x2+3)
Area = (x2)(2x2) + (x2)(3)
Area = 2x4+ 3x2

24. Area and Perimeter
A triangle has sides with lengths of 2x2+4, 4x2+y, and 2x-3y. Write and simplify an expression for the perimeter of the triangle.

25. Perimeter
2x2+4
4x2+y
2x-3y

26. Perimeter
Perimeter = side + side + side
Perimeter = 2x x2+y + 2x-3y
Perimeter = 6x2+2x – 2y + 4

27. Area
2x2+4x +3
Height 2x
Base

28. Area Area = ½ (base x height) Area = ½ (2x) (2x2+4x+3)
Area = ½((2x)(2x2) + (2x)(4x)+ (2x)(3))
Area = ½ (4x3+ 8x2+6x)
Area = 4x3 + 8x2 + 6x 2 2 2
Area = 2x3+ 4x2+3x