1. Regents Review #1
Expressions

2. Simplifying Expressions
What does it mean to simplify an expression?
CARRY OUT ALL OPERATIONS!
PEMDAS is always in effect!

3. Simplifying Exponential Expressions
1) xy0 2) (2x2y)(4xy3) ) (2x3y5)4
24(x3)4(y5)4
16x12y20
x(1) x
8x3y4
multiply coefficients and add exponents
any nonzero number raised to the zero power equals 1
raise each factor to the power

4. Simplifying Exponential Expressions4) 5) 6)
divide coefficients
subtract exponents
move negative exponents and rewrite as positive
raise numerator and
denominator to the power
of the fraction
simplify numerator and denominator coefficients by dividing by a common factor

5. Simplifying Exponential Expressions
When simplifying exponential expressions, remember…
Use exponent rules to simplify
When dividing, all results appear in the numerator. Change negative exponents to positive by moving them to the other part of the fraction
No decimals or fractions are allowed in any part of the fraction

6. Scientific Notation Writing numbers in scientific notation
345,000,000 =
2) =

7. Scientific Notation
Multiplying and Dividing Numbers in Scientific Notation 3) 4)

8. Polynomials When adding polynomials, combine like terms!
(3x – 2) + (5x – y) + (2x – 4)
3x + 5x + 2x – 2 – 4 – y
10x – 6 – y

9. Polynomials
When subtracting polynomials, distribute the minus sign before combining like terms!
Subtract 5x2 – 2y from 12x2 – 5y
12x2 – 5y – (5x2 – 2y)
12x2 – 5y – 5x2 + 2y
12x2 – 5x2 – 5y + 2y
7x2 – 3y

10. Polynomials
When multiplying polynomials, distribute each term from one set of parentheses to every term in the other set of parentheses “double distribute”. 3)

11. Polynomials
When dividing polynomials, each term in the numerator is divided by the monomial that appears in the denominator. 4)

12. What does it mean to factor? Create a “multiplication problem”.
Factoring
What does it mean to factor? Create a “multiplication problem”.

13. Factoring There are three ways to factor Factor out the GCF
AM factoring
3) DOTS

14. Factoring
When factoring completely, factor until you cannot factor anymore! 1) 2) 3)

15. Rational Expressions 1)
When simplifying rational expressions (algebraic fractions), factor and divide out factors that are common to both the numerator and denominator. 1)

16. Rational Expressions 2) 3)
When multiplying, factor and cancel out common factors in the numerators and denominators of the product. 2)
When dividing, multiply by the reciprocal, then factor and divide out common factors in the numerators and denominators of the product. 3)

17. Rational Expressions
When adding and subtracting rational expressions, find a common denominator
Create equivalent fractions using the common denominator(Multiply by FOOs)
Add or subtract numerators and keep the denominator the same
Simplify your final answer if possible
FORM OF ONE
Ex:

18. Rational Expressions 4)
Multiply by FOO
Multiply by FOO
simplified

19. Radicals
When simplifying radicals, create a product using the largest perfect square (4,9,16,25,36,49.64,81,100). 1)
When multiplying radicals, multiply coefficients and multiply radicands. 2)

20. Radicals
When dividing radicals, divide coefficients and divide radicands. 3)
A fraction is not simplified, if a radical appears in the denominator! 4)

21. Radicals
When adding or subtracting radicals, simplify all radicals. If radicals have “like” radicands, then add or subtract coefficients and keep the radicands the same. 5)

22. Writing Algebraic Expressions
1) Express the cost of y shirts bought at x dollars each. xy
Express “three times the quantity of 4 less than a number” as an expression.
3(x – 4)

23. Evaluating Algebraic Expressions
Evaluate x2 – y when x = -2 and y = -5 x2 – y (-2)2 – (-5)

24. Now it’s your turn to review on your own
Now it’s your turn to review on your own! Using the information presented today and your review packet, complete the practice problems in the packet. Regents Review #2 is FRIDAY, May 10th BE THERE!!!!