1. Expressions Regents Review #1 Roslyn Middle School
Research Honors Integrated Algebra

2. Simplifying Expressions
What does it mean to simplify an expression?
CARRY OUT ALL OPERATIONS!

3. Simplifying Exponential Expressions
1) xy0 2) (2x2y)(4xy3) ) (2x3y5)4
x(1) 8x3y (x3)4(y5)4
x x12y20
any nonzero number multiply coefficients raise each factor to
raised to the zero power add exponents to the power
equals one

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. If negative exponents appear in the numerator, move them to the denominator and rewrite them with positive exponents.
Never ever allow a decimal to appear in the numerator or denominator of your expression! All expressions should have integer coefficients in the numerator and denominator!!!

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 – 5
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. 3) 4)

11. Polynomials
When dividing polynomials, each term in the numerator is divided by the monomial that appears in the denominator. 5)

12. Factoring
What does it mean to factor? Factoring is the opposite of simplifying. To factor means to create a product from a simplified expression. It is important to know how to factor because it helps you simplify expressions!

13. Factoring There are three ways to factor Pull 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) 2)
When simplifying rational expressions (algebraic fractions), factor and cancel out factors that are common to both the numerator and denominator. 1) 2)

16. Rational Expressions 3) 4)
When multiplying, factor and cancel out common factors in the numerators and denominators of the product. 3)
When dividing, multiply by the reciprocal, then factor and cancel out common factors in the numerators and denominators of the product. 4)

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.

18. Rational Expressions 5)
Multiply by FOO
Multiply by FOO
simplified

19. Rational Expressions 6)
FOO

20. Radicals
When simplifying radicals, create a product using the largest perfect square. 1)
When multiplying radicals, multiply coefficients and multiply radicands. 2)

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

22. 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)
In order to get like radicals, simplify each radical.

23. Writing Algebraic Expressions
1) Express the cost of y shirts bought at x dollars each. xy
2) Express the number of inches in f feet.
12f

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

25. Regents Review #1 Now it’s time to study
Regents Review #1 Now it’s time to study! Using the information from this power point and your review packet, complete the practice problems.