Algebra 1 Glencoe McGraw-Hill JoAnn Evans

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Algebra 1 Glencoe McGraw-Hill JoAnn Evans The Distributive Property And Combining Like Terms Algebra 1 Glencoe McGraw-Hill JoAnn Evans

Negative factors and subtractions cause some students to make errors when they use the distributive property. To avoid this pitfall, we’re going to change all subtractions to addition of a negative before performing the distributive property. -5(x - 2) Change the subtraction to addition of a negative. -5(x +-2) Perform the distributive property. -5x + 10

-3(y - 5) -3(y +-5) -3y + 15 -5y(y + 7) (x – 2)(-4x) -5y2 +-35y Change the subtraction to addition of a negative. -3(y +-5) 2. Perform the distributive property. -3y + 15 Eliminate the double sign in the final answer. -5y(y + 7) (x – 2)(-4x) -5y2 +-35y (x +-2)(-4x) Because the -4 is in parentheses, it must be distributed. -5y2 – 35y -4x2 + 8x

4u(x – 7) 3z(-5z + 1) 4u(x +-7) -15z2 + 3z 4ux + -28u 4ux - 28u Eliminate the double sign in the final answer. 4u(x – 7) 3z(-5z + 1) 4u(x +-7) -15z2 + 3z 4ux + -28u 4ux - 28u 9n(2m – 3) -(x – 8) Put variables in alphabetical order. 9n(2m +-3) -1(x +-8) 18nm + -27n -1x + 8 18mn – 27n -x + 8

the same variables raised to the same powers. A term is a number, a variable, or a product or quotient of numbers and variables. Like terms are terms that contain the same variables, with corresponding variables having the same power. In other words, like terms have the same variables raised to the same powers.

Examples of LIKE terms: 7x and 9x 3xy and -11xy 2x2 and 15x2 -6bc and bc Each pair has the same variables raised to the same power. Examples of UNLIKE terms: x and x2 mn and m2n 3xy and 12xyz The terms are not identical in power and in variables.

A negative coefficient is a coefficient of negative one. In a term that’s the product of a number and a variable, the number is the coefficient of the variable. 12x 12 is the coefficient of x. -3y -3 is the coefficient of y. 5mn 5 is the coefficient of mn. What’s the coefficient of this term? -x2 -1 is the coefficient of x2. A negative coefficient is a coefficient of negative one.

Like terms can be combined by adding or subtracting the coefficients of the terms. 2(x + 6) – 3 2(x + 6) + -3 2x + 12 + -3 2x + 9 3(2x – 8) + 20x 3(2x + -8) + 20x 6x + -24 + 20x 26x - 24 16 – (5x + 3) 16 + -1(5x + 3) 16 + -5x + -3 – 5x + 13 13 + 8y – 7 – 12y 13 + 8y + -7 + -12y -4y + 6

Like terms can be combined by adding or subtracting the coefficients of the terms. w + 14w – 6w 1w + 14w + -6w 9w 12b2 + 9b2 – 22b2 12b2 + 9b2 + -22b2 -1b2 -b2 3a2 + 6a + 4a2 7a2 + 6a 4(6p + 7q – 2p) 4(6p + 7q + -2p) 4(4p + 7q) 16p + 28q

How can you tell if a variable expression is simplified? 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”.

Simplify more complicated expressions: 11 – 2x(z + 3) + 4x – 2 + xz Change all subtractions to addition of a negative. 11 + -2x(z + 3) + 4x + -2 + xz Perform the distributive property. 11 + -2xz + -6x + 4x + -2 + xz Simplify the expression by combining like terms. -2x + -xz + 9 -2x – xz + 9 Eliminate double signs.

Simplify more complicated expressions: x(y + 4) + 15 – 6xy Change all subtractions to addition of a negative. x(y + 4) + 15 + -6xy Perform the distributive property. xy + 4x + 15 + -6xy Simplify the expression by combining like terms. 4x + -5xy + 15 4x – 5xy + 15 Eliminate double signs.