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Simplifying Algebraic Expressions

Learn to identify terms, like terms, and constants, apply the distributive property, and simplify expressions by combining like terms. Understand the basics of algebraic expressions, coefficients, and variables.

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Simplifying Algebraic Expressions

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  1. Simplifying Algebraic Expressions Distribution and Like Terms Section 5.5

  2. 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 ____________.

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

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

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

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

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

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

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

  10. 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

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

  12. Simplifying Expressions • Distribute first (watch for sign of # you are distributing) • Combine like terms

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

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