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