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Algebra 1 Glencoe McGraw-Hill JoAnn Evans Math 8H The Distributive Property And Combining Like Terms (Day 2)

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Remember -- Like terms are terms that have the same variables raised to the same powers. In a term that is the product of a number and a variable, the number is the coefficient of the variable. Like terms can be combined by adding or subtracting their coefficients.

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Terms are separated by addition signs. To determine the terms of a variable expression, you must first change all subtractions to “add the opposite”. 4x 2 + 3x + 9 Three terms: 4x 2, 3x, and 9 -x – 2y – z = -x + - 2y + - z Add the opposite first. Three terms: -x, -2y, and –z -y – 3r = -y + - 3r Two terms: -y and -3r

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Simplify by using the distributive property and then combining like terms. Next, evaluate by substituting in the given value for the variable. 19 – 4x(y – 6) + 5y when y = 2 and x = 3 = 19 + - 4x(y + - 6) + 5y = 19 + - 4xy + 24x + 5y = 19 + - 4(3)(2) + 24(3) + 5(2) = 19 + - 24 + 72 + 10 = 77

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Simplify by using the distributive property and then combining like terms. Next, evaluate by substituting in the given value for the variable. 3x(x – 9) + 4(y + 7) when x = 2 and y = -3 = 3x(x + - 9) + 4(y + 7) = 3x 2 + - 27x + 4y + 28 = 3(2) 2 + - 27(2) + 4(-3) + 28 = 3(4) + - 54 + (-12) + 28 = 12 + - 54 + - 12 + 28 = 40 + - 66 = -26

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Remember about negatives that appear in front of parentheses!! There is an “invisible 1” outside the parentheses. x - (2x + 3) = x – 1(2x + 3) It’s there. Really! = x + - 1(2x + 3) Add the opposite. = x + - 2x + - 3 Distribute. = -1x + - 3 Combine like terms. = -x – 3 Simplify.

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Distributing a Fraction: ⅛(16x + 40) = ⅛(16x) + ⅛(40) = 2x + 5 -¼(12y 2 – 16) = -¼(12y 2 + - 16) = -¼(12y 2 ) + ( -¼)(-16) = -3y 2 + 4 To multiply by ⅛, divide by 8. To multiply by – ¼, divide by -4.

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How can you tell if a variable expression is simplified? It must pass three tests: 1.There are no more parentheses or other grouping symbols left in the expression. 2.There are no like terms that haven’t been combined. 3.There are no “double signs”.

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