1. Warm-up: Write in scientific notation: 0.003481 3,490,000
HW: pg.36 (4, 7, 8, 12, 21, 24, 30, 32, 34, 45, 46)
pg.38 (68, 93, 94)

2. Objective: Operations with Algebraic Expressions
Special Product Patterns
Sum and difference of same terms
Binomial Square
Binomial Cube
Factoring Greatest Common Term

3. Operations With Algebraic Expressions
An algebraic expression of the form axn, where the coefficient a is a real number and n is a nonnegative integer, is called a monomial, meaning it consists of one term.
Examples:
7x2 2xy 12x3y4
A polynomial is a monomial or the sum of two or more monomials.
4x x4 – 3 x2y – xy + y

4. Operations With Algebraic Expressions
Constant terms, or terms containing the same variable factors are called like, or similar, terms.
Like terms may be combined by adding or subtracting their numerical coefficients.
Examples:
3x + 7x = 10x 12xy – 17xy = – 5xy

5. Examples
Simplify the expression

6. Examples
Simplify the expression

7. Examples
Perform the operation and simplify the expression

8. Examples
Perform the operation and simplify the expression

9. Special Products Let a and b be real numbers, variables, or algebraic expressions. Sum and Difference of Same Terms (a - b)(a + b) = a2 - b2 Square of a Binomial: (a + b)2 = a2 + 2ab + b2 (a – b)2 = a2 – 2ab + b2 Cube of a Binomial: (a + b)3 = a3 + 3a2b + 3ab2 + b3 (a – b)3 = a3 – 3a2b + 3ab2 – b3

10. FOIL Method
(3x – 2)2
(3x – 2)(3x – 2)

11. FOIL Method FIRST
(3x – 2)(3x – 2)
9x2

12. FOIL Method OUTER
(3x – 2)(3x – 2)
9x2
- 6x

13. FOIL Method INNER
(3x – 2)(3x – 2)
- 6x
9x2
- 6x

14. FOIL Method LAST
(3x – 2)(3x – 2)
9x2
- 6x
- 6x
+ 4

15. FOIL Method Combine like terms
(3x – 2)(3x – 2)
9x2
- 6x
- 6x +4
9x2 – 12x + 4

16. Multiply: (3x – 2y)3 using (a – b)3 = a3 – 3a2b + 3ab2 – b3
a = 3x and b = 2y
Plug into the formula a3 – 3a2b + 3ab2 – b3
(3x)3 – 3(3x)2(2y) + 3(3x)(2y)2 – (2y)3
Simplify
27x3 – 54x2y + 36xy2 – 8y3

17. The Product of Two Trinomials Multiply: (x + y – 2)(x + y + 2)
=x2 + 2xy + y2 – 4

18. Factoring
Factoring is the process of expressing an algebraic expression as a product of other algebraic expressions.
Example:

19. Factoring
To factor an algebraic expression, first check to see if it contains any common terms.
If so, factor out the greatest common term.
For example, the greatest common factor for the expression
is 2a, because

20. Examples
Factor out the greatest common factor in each expression

21. Factor by Grouping
Factor out the greatest common factor in each group

22. Sneedlegrit: Multiply (2x – 4)3
Summary:
Operations with Algebraic Expressions
Special Product Patterns
Sum and difference of same terms
Binomial Square
Binomial Cube
Factoring Greatest Common Term
Sneedlegrit: Multiply (2x – 4)3
HW: pg.36 (4, 7, 8, 12, 21, 24, 30, 32, 34, 45, 46) pg.38 (68, 93, 94)