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

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

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. x 2 + 5x – 9 The terms are x 2, 5x, and -9

Terms  Terms with higher exponents are written first. 3x 3 + 7x 2 + x + 5 Highest exponent! Next highest! Constant term is written last!

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.

Coefficient  All variables have a coefficient!!!!  If there is no number in front of the variable, the coefficient is 1. x 2 + x – 5 The coefficient of x 2 is 1. The coefficient of x is 1. 11

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. 3y 2 and 4y are NOT like terms.

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

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

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!

Examples 1. 3x + 2y – x + 5y = 2x + 7y 2. 4a 2 – 2b + 6b + 5 = 4a 2 + 4b + 5 3. x 2 + 3x + 4x 2 – 5x = 5x 2 – 2x

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