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Simplifying Algebraic Expressions Distribution and Like Terms Section 5.5

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Notes When a ________ or ________ sign separates an algebraic expression into parts, each part is called a _______. The numerical factor of a term that contains a variable is called the ____________.

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Notes A term without a variable is called a _________. __________ terms contain the same variables to the same powers, such as 3x and 2x.

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Like Terms Like Terms have the EXACT same variables with the same exponents. Like Terms Unlike Terms 2x, -5x 4x, 4y -8, 10 9, 6x 3y², 8y² -5x, 5x² 7xy, -xy 3x²y, 8xy²

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Examples Identify the terms, like terms, coefficients, and constants 1. 4 – 4y + y – 3 2. 7 – 5y + 2 + 1

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Example Find the like terms: 7x, -8, 4y, x, x², 6, 5xy, 8y, 9

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Notes An algebraic expression is in _____________form if it has no like terms and no parentheses.

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Combining Like Terms Terms must be like in order to add and subtract them. To combine like terms: Add the coefficients Keep the variable

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Examples 6x + 5y – 3x + y -2x – 8y + 5x – 4y 5a – 2b + c – 5b + 4b

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Distributive Property Signified by a number next to ( ) with no sign in between Ex: 5(x + 3) Tells you to multiply the number outside by every term inside Watch the signs

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Examples 4(x + 3) (2y – 6)5 a(7b + 2c) -8(4m – 2n)

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Simplifying Expressions oDistribute first (watch for sign of # you are distributing) oCombine like terms

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Examples 3(x + 2) – 4x + 8 2 – 5(2x + 4) + x 2(3x – 4y) – (x – 2y)

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