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. 2x 3 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 x x + 9x 2 = - 2x 2 + 9x 2 + 3x - 15x 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.

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

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. = Multiply. = -37

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

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) = = = 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. = x Take off brackets (addition). = x … 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

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