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Combining Like Terms

This guide explains the concepts of constants, variables, coefficients, and algebraic expressions. It defines constants as unchanging values, such as numbers like pi (3.1415926). Variables represent changing values, like x in different problems, while coefficients indicate quantities, as in 3x. The text contrasts algebraic expressions and equations and introduces terms, including monomials, binomials, and trinomials. Focusing on combining like terms, the guide illustrates how to add coefficients of similar variables, reinforcing the process with clear examples and emphasizing the importance of managing signs correctly.

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Combining Like Terms

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  1. Combining Like Terms

  2. Let’s start with some vocabulary.

  3. Numbers are called constants because their value remains the same, or constant. A 3 in problem #34 means exactly the same thing as a 3 in problem #7.

  4. TheGreek letter, piis a constant even though it is a letter. It always represents exactly the same number 3.1415926… We may round it to different places, depending on how accurate we want to be, but it is always the same number.

  5. A variable is a letter that stands for a number.In one problem, x might stand for 3.In another problem, x might stand for 7.It’s called a variable because its value can change – vary – from problem to problem.

  6. The coefficientof a variable is the number that is written in front of the variable to tell you how many of them there are. In the term 3x, the coefficient of x is 3. It means we have 3 x’s.

  7. If a variable doesn’t have a coefficient, the coefficient is understood to be 1. x = 1x

  8. An algebraic expression is any combination of variables, constants, grouping symbols and arithmetic operations. An algebraic expression does not have an equal sign.

  9. An algebraic expression is like a phrase is in English. An equation has an equal sign. It is like a sentence in English.

  10. Terms are algebraic expressions that are separated by + and – signs that are not inside parentheses. 2x + 2y - 5( x+ 2 ) has 3 terms

  11. A monomial is 1 term: 13xyz or 7( y – 4 ) A binomial is 2 terms: 2x + 3y A trinomial is 3 terms: x + y + z A polynomial has many terms.

  12. Like terms are terms that have the same variable raised to the same power. 2x and 3x are like terms 4y and y are like terms

  13. When you combine like terms, you combine the coefficients and copy the variables. 5x + 3x = 8x

  14. 5x + 2y + 3 – x + y -7 Writing the like terms together: 5x – x + 2y + y + 3 – 7 Combining them gives us: 4x + 3y - 4 You can’t combine constants and variables.

  15. 5( x + 2) –3( x + y – 7) 5x + 10 –3x –3y+ 21 watch your signs! Writing the like terms together: 5x – 3x – 3y + 10 + 21 Combining them gives us: 2x – 3y + 31

  16. Combining like terms is easy! Just pair them up with their buddies!

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