Adding, Subtracting and Multiplying Polynomials

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Adding, Subtracting and Multiplying Polynomials
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Combining Like Terms

• When simplifying we often need to combine like
  terms.
• Like terms are terms with the exact same
  variables with the exact same exponents.
• Which of the following are like terms?

2x
xy
3x²y
5x²y²
-9
6x²y
12xy²
9x
4xy
12x²y²
6
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Combining Like Terms

• Only Like Terms can be added or subtracted
• To Add or Subtract like terms you simply add or
  subtract their coefficients.

They are both like terms so we add their
coefficients (numbers in front). 3 4 7
For example 3x 4x
7x
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What is a polynomial?

• monomial - a number or a product of a number and
  one or more variables with nonnegative integer
  exponents
• Examples -2x, x2y2, a3b4c6
• polynomial - a finite sum of monomials
• Examples x 4, y3 - 6y2 5, 4xy3 2x2y2 3x

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Adding Polynomials

• To add polynomials simply combine the like terms

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Adding Polynomials

• Example 2

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Adding Polynomials

• Try it on your own
• Example 3

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Subtracting Polynomials

• To subtract polynomials, distribute the negative
  then combine like terms

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Subtracting Polynomials

• Example 2

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Subtracting Polynomials

• Try it on your own
• Example 3

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Multiplying Polynomials

• To multiply polynomials you must multiply each
  term in the first polynomial by each term in the
  second polynomial. Then combine like terms.
• Following are three ways to do this

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Method 1

• Similar to the distributive property you multiply
  each term in the first polynomial by each term in
  the second polynomial

xx²
x2xy
yx²
y2xy
xy²
yy²
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Method 2
yy²
y2xy
yx²
xy²
x2xy
xx²
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Method 3

• The box method

xx²
xy²
x2xy
y2xy
yx²
xx²
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Examples
x²x²
x²2x
1x²
12x
x²-3
1-3
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More Examples
x²2x²
-x2x²
12x²
x²2x
12x
-x2x
x²-3
1-3
-x-3
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More Examples
2x2x
2x-y
-y2x
-y-y