9 March 2011

9 March 2011

Algebra 2

Algebraic Operations 3/9• Like Terms Terms are considered “like” if they

have the same variable AND the same powers on the variable.

Mathematics.XEI.303: (16-19) Combine like terms

https://cim.cps.k12.il.us/Assess/Controls/SelectControls/



Algebraic Operations 3/9• Like Terms Terms are considered “like” if they

have the same variable AND the same powers on the variable.

Example: x2, 2x, 5x3, 8x2

Only x2, 8x2 are like terms





Which of the following are like terms?

1 2 3 4 5

0% 0% 0%0%0%

1. 2x and2x2

2. 3x and 33. 4x2 and 4x3

4. 5x3 and 8x3

5. x and xy

0 of 30

60

Algebraic Operations 3/9• Like Terms When you are combining like terms,

add the coefficients.







Example: 2xy + xy + 5xy = ?








2 + 1 + 5 = 8








2 + 1 + 5 = 8, so

2xy + xy + 5xy = 8xy





2a3 + a2 + a + 3a – 4a3 = ?

1 2 3 4

0% 0%0%0%

1. a9

2. 2a7 - 4a3

3. 2a3 + a2 + 4a4. -2a3 + a2 + 4a

0 of 30

60

2a3 + a2 + a + 3a – 4a3 = ?

2a3 + a2 + a + 3a – 4a3 = ?Combine like

terms-2a3 + a2 + 4a

Like Terms:

• Choose any 10 questions from the first 15• Write the question #, show your work, and

write the letter answer choice on your sheet• You have 10 minutes.

09000 01 87654321590 04 98765432103 9876543210987654321021 987654321098765432100Hours Minutes Seconds

Time Left

Algebraic Operations 3/9• Exponent

RulesYou can multiply or divide the same variable, even if the powers are different.

Mathematics.NCP.604: (28-32) Apply rules of exponents





RulesYou can multiply or divide the same variable, even if the powers are different.

Multiplication: Add exponentsDivision: Subtract exponents

Example: (x2)(x3)(x5)(x7) = ?






RulesExample: (x2)(x3)(x5)(x7) = ?







Add all the exponents on ‘x’

2 + 3 + 5 + 7 = 17







Add all the exponents on ‘x’

2 + 3 + 5 + 7 = 17

(x2)(x3)(x5)(x7) = x17






RulesExample 2:

5

23

xyyx






RulesExample 2:

Larger x is on top, subtract the bottom power from the top power:

5

23

xyyx

5

22

yyx






RulesExample 2:

Larger x is on top, subtract the bottom power from the top power:

Larger y is on bottom, subtract the top power from the bottom power:

5

23

xyyx

5

22

yyx

3

2

yx





(xy2)(x3y2) = ?

1 2 3 4 5

0% 0% 0%0%0%

1. x3y4

2. x2y3. x4y4

4. xy7

5. xy8

0 of 30

60

(xy2)(x3y2) = ?

• (xy2)(x3y2) = ?

x4

(xy2)(x3y2) = ?

• (xy2)(x3y2) = ?

x4y4


RulesIf you are raising a variable with an exponent, multiply the powers.

Example: (a3)4







Example: (a3)4

3*4 = 12







Example: (a3)4

3*4 = 12

(a3)4 = a12





Exponent Rules:

• Complete ten questions out of # 16-30• Write the question #, show your work, and



Time Left:

Algebraic Operations 3/9• Adding

FractionsIf you are adding two fractions with the SAME denominator:

?64xx

Mathematics.NCP.201: (13-15) Recognize equivalent fractions






Add the numerators together.

?64xx







Add the numerators together.4 + 6 = 10

?64xx







Add the numerators together.4 + 6 = 10

?64xx

xxx1064





.

1 2 3 4 5

0% 0% 0%0%0%

1. 7x/62. 7x/33. 10x/94. 10x/65. 10x/3

?35

32

xx

0 of 30

60


FractionsIf you are adding two fractions with a different denominator:

?53

yx

Mathematics.NCP.501: (24-27) Find and use the least common multiple






Multiply the denominators:

?53

yx

xyyx?53







Cross Multiply

?53

yx

xyyx

yx3553





Adding Fractions:

• Complete # 31-40• Write the question #, show your work, and



Time Left

Simplifying Expressions 3/8

Simplify 3(2q + r)

Mathematics.XEI.402: (20-23) Add and subtract simple algebraic expressions






Simplify 3(2q + r)

6q + 3r + 20q – 35r







Simplify 3(2q + r)

6q + 3r + 20q – 35r






Notes: Multiplying Binomials 3/8Box Method You can use the box method to

multiply two binomials:

Example 1: (x + 4)(x – 3)

Make a 2x2 square box

XEI.405:Multiply 2 Binomials



Example 1: (x + 4)(x – 3)

Write the first binomial across the top x +4




Example 1: (x + 4)(x – 3)

Write the second binomial going down x +4x

-3




Example 1: (x + 4)(x – 3)

Multiply x*x x +4x x2

-3




Example 1: (x + 4)(x – 3)

Multiply x*4 x +4x x2 +4x

-3




Example 1: (x + 4)(x – 3)

Multiply -3*x x +4x x2 +4x

-3 -3x




Example 1: (x + 4)(x – 3)

Multiply -3*4 x +4x x2 +4x

-3 -3x -12




Example 1: (x + 4)(x – 3)

List each term inside the box x +4x x2 +4x

-3 -3x -12

x2 + 4x – 3x - 12XEI.405:Multiply 2 Binomials



Example 1: (x + 4)(x – 3)

Simplify x +4x x2 +4x

-3 -3x -12

x2 + 4x – 3x – 12 = x2 + x - 12XEI.405:Multiply 2 Binomials

Multiplying Expressions:

• Complete # 41-50• Write the question #, show your work, and



Time Left

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9 March 2011

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