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Simplifying Expressions

XEI 303: Combine like terms (e.g., 2x + 5x) XEI 601: Manipulate expressions and equations. Simplifying Expressions. Definitions - Term. Term - a number (constant term), a variable (algebraic term), or a combination of numbers or variables that are added to form an expression.

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Simplifying Expressions

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  1. XEI 303: Combine like terms (e.g., 2x + 5x) XEI 601: Manipulate expressions and equations Simplifying Expressions

  2. Definitions - Term • Term - a number (constant term), a variable (algebraic term), or a combination of numbers or variables that are added to form an expression. x2 + 5x – 9 The terms are x2, 5x, and -9

  3. Terms • Terms with higher exponents are written first. 3x3 + 7x2 + x + 5 Highest exponent! Next highest! Constant term is written last!

  4. Definitions - Coefficient • Coefficient – when a number and a letter is linked together by multiplication; the number is called the coefficient. 2x² + 8x – 9 The coefficient of x² is 2. The coefficient of x is 8. -9 is the constant term.

  5. Coefficient • All variables have a coefficient!!!! • If there is no number in front of the variable, the coefficient is 1. x2 + x – 5 The coefficient of x2 is 1. The coefficient of x is 1. 1 1

  6. Definitions – Like Terms • Like Terms - are terms that share the same variable(s) and are raised to the same power. 2x and 5x are like terms. 3y2 and 4y are NOT like terms.

  7. Like Terms 3x2 + 4y – 5x2 + 5 – 2y I’m +3x2 Highest exponent! Like Terms!!! Like Terms!!! Like Terms!!! Notice the sign belongs to the term that follows it! +4y, -5x2, +5, -2y

  8. Definitions - Combining Like Terms • Combining Like Terms - the process of adding or subtracting like terms. 3x2 + 4y – 5x2 + 5 – 2y So we end up with: -2x2 + 2y + 5 Like Terms!!! 3x2 – 5x2 = -2x2 4y – 2y = 2y

  9. The Distributive Property Revisited… You may have to use the distributive property before simplifying! 2(3x – 5) + 5(x + 4) 6x – 10 + 5x + 20 11x + 10 Distribute! Add like terms!

  10. Examples 1. 3x + 2y – x + 5y = 2x + 7y 2. 4a2 – 2b + 6b + 5 = 4a2 + 4b + 5 3. x2 + 3x + 4x2 – 5x = 5x2 – 2x

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