3C  0  day 2  Equations.notebook

1

Learning Goal:Expand and Solve Simple Equations

equations

Collecting Like Terms

    - add or subtract the ____________________ of the terms that have the same ______________ and ________________

3a + 5a 3a2 + 4a + 5a2 +7a

2ab + 3a2b + 5ab -7ab2

3C  0  day 2  Equations.notebook

2

Multiplying Powers

Dividing Exponents

- add _________________

- ______________ the exponents

(3a4b7)(5a2b3)

Distributive Property

- rainbow- _________________ everything in one

bracket with ______________ in the other bracket

(3a)(5a2 + b3) (3a + 2b)(5a + b)

3C  0  day 2  Equations.notebook

3

Solving Equations

1. Eliminate fractions by multiplying everything by the ______________ denominator.

2. Eliminate brackets by using ______________3. Move all variables to one side.

a. identify ___________b. identify order (___________BEDMAS)

c. do the ______________d. do it to __________ sides

x+5=7 2x+5=7

3C  0  day 2  Equations.notebook

4

On the Boards...

2x+5=3x-2 2x+5=5x-7

2x2+5=23

Homework

Handout

3C  0  day 2  Equations.notebook

5

Handout

3C  0  day 2  Equations.notebook

6

Attachments

0.5.5 Expanding & Solving Equations Review.doc

0.5.5 Pythagorean Theorem Review.doc

Expanding & Solving Equations Practice.doc

Expanding & Solving Equations Review.pdf

Pythagorean Theorem Practice.doc

Pythagorean Theorem Review.pdf

Fractions Practice Solutions.pdf

Operations Practice Solutions.pdf

MBF3C – Diagnostic Review

Date: _________________________

Expanding and Solving Equations Review

1. COLLECT LIKE TERMS

Add or subtract the _____________________ of terms that have the same _________________ and _________________________

aa

+=

23

Example 1:

abab

--+

325

Example 2:

xxxx

+--++

22

236457

2. DISTRIBUTIVE PROPERTY (RAINBOW)

Multiply each term of the _____________________ by the _____________________

()

abc

+=

Example 1:

()

aab

--

232

Example 2:

()

xxyy

---

283

3. MULTIPLY BINOMIALS (FOIL)

F: Multiply the _______________ terms in each bracket together

O: Multiply the _______________ terms in each bracket together

I: Multiply the _______________ terms in each bracket together

L: Multiply the _______________ terms in each bracket together

()()

abcd

++=

Example 1:

()()

abab

+--

2432

Example 2:

()()

xxx

-+

2

235

4. SOLVING LINEAR EQUATIONS ALGEBRAICALLY

· Eliminate fractions by multiplying each ____________ in the equation by the ____________

· Eliminate any brackets by using the ____________________________________

· _________________ the equation to ____________________________________ and solve

Example 1:

()()

xxx

-+-=-

323425

Example 2:

yy

--

=

72

34

**Remember to collect like terms if possible**

Very similar to the �Distributive Property (Rainbow Method)

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SMART Notebook

MBF3C – Diagnostic Review

Date: ___________________________

Pythagorean Theorem Review

Definition: The Pythagorean Theorem

In a _______________________ triangle, the ___________ of the squares of the two _________ (the two sides that form the __________________________) equals the ________________ of the ___________________________

Examples:

Find the unknown values. Round to one decimal place.

a)

b)

59o

(

y

6 cm

7 cm

x

31o

(

5 cm

3 cm

Formula:

SMART Notebook

MBF3C – Diagnostic Review

Date: _________________________

Expanding and Solving Equations Practice

1. Simplify

a)

xyxy

--+

3275

b)

xxxxxx

-+-+-

3232

3422

c)

()()()

xyxyxy

--+-+

456372

d)

()

mnppmn

+--

22

23

2. Expand

a)

()

xy

+-

3252

b)

()

xxxy

-+

2

5

c)

()

mmn

-

22

32

d)

()

xyxyxy

-

53245

42

3. Expand and Simplify

a)

()()

xxxx

++-

3252

b)

()()

hhhh

-+--

725453

c)

()()

mnmnmnmn

--+

2323

2534

d)

()()

xyxyxyyx

-+++--+

33

35212327

e)

()()

xx

-+

3245

f)

()()

yy

-+

7324

g)

()()

xyxy

-+

574

h)

()()

xyxy

-+

3232

3452

4. Solve

a)

xx

-=+

68410

b)

..

x

+=

27894

c)

m

=-

1352

d)

..

mm

-=+

13525415

e)

()()

yy

-=+

8144

f)

()()

rr

-=-

45321

g)

x

=

20

5

h)

x

=

2

8

5

i)

y

-=

12

3

23

j)

mm

-=+

45

32

k)

xx

+-

=

2423

53

l)

xx

xx

+-

=

241

2

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SMART Notebook

SMART Notebook

MBF3C – Diagnostic Review

Date: ____________________________

Pythagorean Theorem Practice

1. For each right triangle, solve for the unknown side and angle. Round answers to one decimal.

a)

b)

c)

d)

2. Find the value of each unknown measure to the nearest hundredth.

a)

a

=+

222

513

b)

p

=+

222

106

c)

b

+=

222

1121

d)

..

y

+=

222

2345

3. Determine the length of the diagonals of each rectangle to the nearest tenth.

a)

b)

4. An apartment building casts a shadow. From the tip of the shadow to the top of the building is 100m. The tip of the shadow is 72 m from the base of the building. How tall is the building?

4.2 m

1.3 m

6 cm

3 cm

53o

(

b

5 cm

3 cm

45o

(

h

3 cm

3 cm

40o

(

y

9 cm

14 cm

x

30o

(

7 cm

4 cm

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SMART Notebook

SMART Notebook

SMART Notebook

SMART Notebook

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