Regents Review #1

Expressions

Roslyn Middle SchoolResearch Honors Integrated Algebra

Simplifying Expressions

What does it mean to simplify an expression?

CARRY OUT ALL OPERATIONS!

Simplifying Exponential Expressions

1) xy0 2) (2x2y)(4xy3) 3) (2x3y5)4

x(1) 8x3y4 24(x3)4(y5)4

x 16x12y20

any nonzero number multiply coefficients raise each factor toraised to the zero power add exponents to the power equals one

Simplifying Exponential Expressions

4)3

3

2

y

x2

24

xy

yx 6)5)

14 xy

y

x4

divide coefficientssubtract exponentsmove negative exponents and rewrite as positive

9

6

y

x

6

9

x

y

raise numerator and denominator to the powerof the fraction

3

3

24

4

xy

yx

6

1 22 yx

2

2

6y

x

simplify numerator and denominator coefficients by dividing by a common factor

Simplifying Exponential Expressions

When simplifying exponential expressions, remember…

1)Use exponent rules to simplify

2)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.

3)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!!!

Scientific Notation

Writing numbers in scientific notation

1)345,000,000 = 3.45 108

2) 0.0000109 = 1.09 10-5

Scientific Notation

Multiplying and Dividing Numbers in Scientific Notation3)

3

41

4

95

95

1028.1

101028.1

108.12

10102.34

102.3104

18

6

12

6

12

104.1

10

10

4

6.5

104

106.5

4)

Polynomials

When adding polynomials, combine like terms!

1)(3x – 2) + (5x – y) + (2x – 4)

3x + 5x + 2x – 2 – 4 – y

10x – 6 – y

PolynomialsWhen subtracting polynomials, distribute the minus sign before combining like terms!

2)Subtract 5x2 – 2y from 12x2 – 5

12x2 – 5y – (5x2 – 2y)

12x2 – 5y – 5x2 + 2y

12x2 – 5x2 – 5y + 2y

7x2 – 3y

PolynomialsWhen multiplying polynomials, distribute each term from one set of parentheses to every term in the other set of parentheses.

8103

82123

423

2

2

xx

xxx

xx

485

46223

232

23

223

2

xxx

xxxxx

xxx

3)

4)

PolynomialsWhen dividing polynomials, each term in the numerator is divided by the monomial that appears in the denominator.

24

2

23

2

42

2

2342

4

3

12

3

3

3

123

xyy

x

yx

x

yx

x

yxyx

5)

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!

Factoring

There are three ways to factor

1)Pull out the GCF

2)AM factoring

3) DOTS

)12(224 2 xxxx

)2)(3(652 xxxx

)43)(43(169 2242 yxyxyx

FactoringWhen factoring completely, factor until you cannot factor anymore!

)2)(3(2

)65(2

121022

2

xx

xx

xx1)

)3)(3(4

)9(4

36422

22

yxyx

yx

yx

)1)(2(1

1)2(1

22

2

xx

aoutpullxx

xx

2)

3)

Rational Expressions

When simplifying rational expressions (algebraic fractions), factor and cancel out factors that are common to both the numerator and denominator.

1) 23

)2(3

3

63

x

xx

2)1)1)(2(

)2(

23

22

2

x

x

xx

xx

xx

xx

Rational Expressions

3)

When multiplying, factor and cancel out common factors in the numerators and denominators of the product.

)2)(1(

)5(

)2)(4()1(

)4)(5(

82

2022

2

xx

x

xx

x

xx

xx

xx

x

xx

xx

4)

When dividing, multiply by the reciprocal, then factor and cancel out common factors in the numerators and denominators of the product.

)4(

)1)(2(

)4)(2(

)1)(1(

)1(

)2)(2(

86

1

1

4

1

86

1

42

22

2

22

x

xx

xx

xx

x

xx

xx

x

x

x

x

xx

x

x

Rational Expressions

1) When adding and subtracting rational expressions, find a common denominator.

2) Create equivalent fractions using the common denominator(Multiply by FOOs)

3) Add or subtract numerators and keep the denominator the same.

4) Simplify your final answer if possible.

Rational Expressions

5)

22

22

2

22

9

)32(2

9

649

6

9

43

2

9

4

93

2

9

4

x

x

x

xxx

xxx

xLCDxx

33

xx

simplified

Multiply by FOO Multiply by FOO

Rational Expressions

6)

)2)(4(

1297

)2)(4(

1287

)2)(4(

)1(287

)2)(4(

1

)2)(4(

)4(7

)2)(4(

1

2

7

)2)(4()2)(4(

1

2

7

82

1

2

7

22

2

2

xx

xx

xx

xxx

xx

xxx

xx

x

xx

xx

xx

x

x

x

xxLCDxx

x

x

x

xx

x

x

x

4x4x

FOO

Radicals

When simplifying radicals, create a product using the largest perfect square.

1) 3431648

When multiplying radicals, multiply coefficients and multiply radicands.

2) 3303215341512156523

Radicals

When dividing radicals, divide coefficients and divide radicands.

3) 635

30

2

6

52

306

A fraction is not simplified, if a radical appears in the denominator!

4)

2

23

2

2

2

3

2

3

fooabymultiply

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)

24

21228

234242

2942162

184322

In order to get like radicals, simplify each radical.

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

Evaluating Algebraic Expressions

Evaluate x2 – y when x = -2 and y = -5

x2 – y (-2)2 – (-5)

4 + 5

9

)(innumbersnegativeputalways

Regents Review #1

Now it’s time to study!

Using the information from this power point and your review packet,

complete the practice problems.