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Combining Like Terms

Combining Like Terms. Let’s start with some vocabulary. 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. The Greek letter, pi is a constant even though it is a letter.

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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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