Welcome to the MM204

Unit 4 Seminar

Section 2.7: Combining Like Terms

Like Terms: Exactly the same letter and the same exponent. We need like terms to add and subtract.

Example: 3x and 5x are like terms.

2x3 and 4x are not like terms.

Like Terms Examples

3x + 8x = 11x

8x + 7y + 2x - 4y = 8x + 2x + 7y – 4y Rearrange if it helps.= 10x + 3y

Like Terms Example

3x + 5 - 2x2 + 1 - 15x + 9x2

= - 2x2 + 9x2 + 3x - 15x + 5 + 1

I like to rearrange the terms so the like terms are together. This is optional for you.

= 7x2 – 12x + 6

We add (subtract) the numbers in front of the letters and keep the letters the same.

Like Terms Example

Rearrange the terms (optional).

Get LCDs since we’re adding.

yxyx107

61

43

21

yyxx107

43

61

21

yyxx

22

107

55

43

61

33

21

yyxx2014

2015

61

63

yx2029

64

yx2029

32

Section 2.8: Evaluating Expressions and Formulas

Evaluating Expressions: We’ll be given an expression and a number to plug in for the

letter(s). Plug in and simplify.

Example: Evaluate 3x - 10y; for x = 1 and y = 4

= 3(1) - 10(4) Substitute the given values into the expression.

= 3 - 40 Multiply.

= -37

The Importance of Parentheses

2y2 for y = -4= 2(-4)2 We are taking y to the second power.= 2(-4)(-4)= 2(16)= 32

(2y)2 for y = -4= (2(-4))2 We are taking 2y to the second power.= (-8)2

= (-8)(-8)= 64

Evaluating an Expression Example

Evaluate 2x2 - 5x + 3y2 for x = -2 and y = 4

= 2(-2)2 – 5(-2) + 3(4)2 PEMDAS.

= 2(-2)(-2) - 5(-2) + 3(4)(4)

= 2(4) - 5(-2) + 3(16)

= 8 + 10 + 48

= 18 + 48

= 66

Formulas Example

#42 on page 101: A field is shaped like a parallelogram. The base measures 92 feet. The altitude measures 54 feet. What is the area of the field?

Formulas Example

We want to build a fence to enclose a garden. The garden is a rectangle with a width of 10 feet and a length of 23 feet. How much fencing do we need to buy?

Section 2.9: Grouping Symbols

Grouping Symbols Instead of using parentheses all the time, we can use brackets and

braces, too. We start with the innermost set of symbols and work our way out.

Example: 2 + [3 + 2(x + 5)]

= 2 + [3 + 2x + 10] Use Dist. prop. on innermost set.

= 2 + [13 + 2x] Combine like terms inside brackets.

= 2 + 13 + 2x Take off brackets (addition).

= 15 + 2x … or… 2x + 15 Combine like terms.

Grouping Symbols Example

Example: 4(x - y) - 2(3x + y)

Use the distributive property to get rid of the parentheses.

= 4x - 4y - 6x - 2y

combine like terms

= -2x - 6y

Grouping Symbols Example

2a - {6b - 4[a - (b - 3a)]} Start with the innermost set of parentheses.

= 2a - {6b - 4[a - b + 3a]}

= 2a - {6b - 4[4a - b]} Combine like terms inside.

= 2a - {6b - 16a + 4b} Use the dist prop to get rid of the brackets.

= 2a - {10b - 16a} Combine like terms.

= 2a - 10b + 16a Get rid of the braces.

= 18a - 10b

Thanks for Participating!

AIM: tamitacker

Read, read, read!

Email me if you have questions.