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Introduction to Combining Like-Terms
Mrs. Cheyenne’s Mathematics Class
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
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
4 ² = 16
5² = 25
1 ³ = 1
2³ = 8
3³ = 27
4³ = 64
5³ = 125
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
Adding▪ Simplify before combining ▪ Exponents must match to combine▪ Variables in front of the exponent must match▪ You will only add numbers
▪ Exponents can be paired with variables and numbers▪ 6x yz⁴ ²▪ Matching exponents do not change in value
• 3x²+10x²+6x
• 13x²+6x
Example 1
• x³+1³+2+9
• x³+12
Example 2
• 7xy³+yx²+x²
• 7xy³+yx²+x²
Example 3
???
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
• xz²-2xz²+xz
• -xz²+xz
Example 1
•5x²y
•ØExample 2
• 24z³-24z +1³
• 1
Example 3
? ? ?
Multiplying▪ Simplify first▪ All variables have an exponent ▪ Exponents are added: x · x = x ²▪ Exponents must match to be combined: x · -2x² ≠ -x ³
▪ Some equations require number properties ▪ The distributive property will be used the most ▪ Don’t forget to keep signs in order
• 2x²y·6x²y
• 12x⁴y²
Example 1
• 7z ·² 2z
• 7z ·² 2z
Example 2
• 25 – (x + 3 – x2)
• x2 – x + 22
Example 3
? ? ?
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
• +
• x
Example 1
• + xy z²• x²yz+xy²z
Example 2
• -(-xy)
• 10xy
Example 3
? ? ?
Mixed: a little bit of everything
÷×
+_𝟓𝒚
𝟐𝒚−𝒚 ²
𝟐 𝒙 𝒚𝟑
𝟒 𝒚 𝒙𝟔
-12x³+12x³
6x-4yx+x
2z(z+x)-z
3x(y-5y)+xy
10xy²z+y² 5x²+3x²+12-5
-16x²+8x²
𝟑𝟐𝒙 ³𝟖 𝒙
· 𝒚𝒛
Works CitedGreen 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 fromhttp://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