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Introduction to Combining Like-Terms

Introduction to Combining Like-Terms. Mrs. Cheyenne’s Mathematics Class. TE S T!. ● What balloons are alike? ● Which are different? ● Can you make it into an equation ? 8b+7g If you can do this you can combine like-terms. Click. What are like-terms ?.

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Introduction to Combining Like-Terms

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  1. Introduction to Combining Like-Terms Mrs. Cheyenne’s MathematicsClass

  2. TEST! ●What balloons are alike? ●Which are different? ● Can you make it into an equation? 8b+7g If you can do this you can combine like-terms Click

  3. What are like-terms? ▪ Numbers/variables in an equation that are the same ▪ Combine by subtracting, multiplying, dividing, and/or multiplying ▪ Combining like-terms condenses the equation ▪ Variables are usually x, y, z ▪ Combining like-terms since kindergarten: 1+2=3 ▪ Exponents will be involved with like-terms ▪ Only possible when equation is a polynomial 1² = 1 2² = 4 3² = 9 4² = 16 5² = 25 1³ = 1 2³ = 8 3³ = 27 4³ = 64 5³ = 125

  4. Polynomials 101 ▪ Equations with more than one term ▪Terms can be numbers, variables, or both: ▪ Not every polynomial will have like-terms ▪ Variables can be seen as x, y, z, xy, yz, xz, or xyz ▪ Most equations require being solved more than one way ▪ Exponents play a huge part in combining like-terms ▪ Squared (²) and cubed (³) is what you will see

  5. Adding ▪ Exponents can be paired with variables and numbers ▪ 6x⁴yz² ▪ Matching exponents do not change in value ▪ Simplify before combining ▪ Exponents must match to combine ▪ Variables in front of the exponent must match ▪ You will only add numbers ? ? ?

  6. Subtracting ▪ Simplify before combining ▪ Exponents do not change when combining ▪ 5x³ - 4x³ = x³ ▪ Exponents must match to combine ▪ Negative numbers will be seen a lot ▪ Negative signs are in front of a number ▪ Do not change position of terms ? ? ?

  7. Multiplying ▪ Simplify first ▪ All variables have an exponent ▪ Exponents are added: x· x= x² ▪ Exponents must match to be combined: x · -2x²≠-x³ ▪ Some equations require number properties ▪ The distributive property will be used the most ▪ Don’t forget to keep signs in order ? ? ?

  8. Dividing ▪ Always simplify first ▪ Exponents are subtracted when simplifying ▪ Rule of thumb: largest value exponent goes first: ▪ 6x⁴ + 4xz³ – 18y² – yz ▪ Fractions should be shown with horizontal line ▪ Top exponents are subtracted by those on bottom ▪ Exponents don’t have to match to subtract ? ? ?

  9. Mixed: a little bit of everything _ × -16x²+8x² 2z(z+x)-z + ÷ 5x²+3x²+12-5 10xy²z+y² 3x(y-5y)+xy -12x³+12x³ 6x-4yx+x

  10. Works Cited Green and blue balloons. n.d.[Photograph]. Retrieved September 2013 from http://www.donors1.org/second-chance- blog/?attachment_id=1646 Hill, B. (2009). The science of the beard. [Photograph]. Retrieved September 2013 from http://whiskerino.org/2009/beards/brandonhill/4434/ Hohomann, A. n.d.Collect like terms. [Image]. Retrieved September 2013 from http://ahohmann.wikispaces.com/Math+8 Patsay, I. n.d.Seamlessly vector wallpaper mathematics on white. [Image]. Retrieved September 2013 from http://www.123rf.com/photo_5119710_seamlessly- vector- wallpaper-mathematics-on-white.html

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