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**Algebra 1 Glencoe McGraw-Hill JoAnn Evans**

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

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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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**= -x + -2y + -z Add the opposite first.**

Terms are separated by addition signs. To determine the terms of a variable expression, you must first change all subtractions to “add the opposite”. 4x2 + 3x Three terms: 4x2, 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 = x(y + -6) + 5y = xy + 24x + 5y = (3)(2) + 24(3) + 5(2) = = 77

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**3x(x – 9) + 4(y + 7) when x = 2 and y = -3 = 3x(x + -9) + 4(y + 7) **

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 x + 4y + 28 = 3(2) (2) + 4(-3) = 3(4) (-12) + 28 = = = -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 Distribute. = -1x Combine like terms. = -x – Simplify.

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**Distributing a Fraction:**

To multiply by ⅛, divide by 8. ⅛(16x + 40) = ⅛(16x) + ⅛(40) = 2x + 5 -¼(12y2 – 16) = -¼(12y ) = -¼(12y2) + ( -¼)(-16) = -3y2 + 4 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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