1 Algebra 1 Glencoe McGraw-Hill JoAnn Evans Math 8HThe Distributive PropertyAndCombining Like Terms(Day 2)Algebra Glencoe McGraw-Hill JoAnn Evans
2 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.
3 = -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
4 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
5 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
6 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.
7 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 + 4To multiply by – ¼ ,divide by -4.
8 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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