1. Welcome to the MM204 Unit 4 Seminar

2. 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. 2x 3 and 4x are not like terms.

3. Like Terms Examples 3x + 8x = 11x 8x + 7y + 2x - 4y = 8x + 2x + 7y – 4y Rearrange if it helps. = 10x + 3y

4. Like Terms Example 3x + 5 - 2x 2 + 1 - 15x + 9x 2 = - 2x 2 + 9x 2 + 3x - 15x + 5 + 1 I like to rearrange the terms so the like terms are together. This is optional for you. = 7x 2 – 12x + 6 We add (subtract) the numbers in front of the letters and keep the letters the same.

5. Like Terms Example Rearrange the terms (optional). Get LCDs since we’re adding.

6. 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

7. The Importance of Parentheses 2y 2 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

8. Evaluating an Expression Example Evaluate 2x 2 - 5x + 3y 2 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

9. 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?

10. 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?

11. 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.

12. 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

13. 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

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