5.2 Like and Unlike Terms

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5.2 Like and Unlike Terms
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Zero Pairs

• When you work with integers, if you combine -1
  and 1, it would be zero.
• What do you think happens when you combine
  algebra tiles with opposite signs?
• A 1 tile and a 1 tile form a zero
  pair.
• We can use zero pairs to simplify polynomials.

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Write the integer modeled by each set of tiles.

• ________
• ________

2
-3
4

• Terms that can be represented by algebra tiles
  with the same size and shape are called like
  terms.
• Like terms have the same variables, and/or the
  same exponent.
• Like terms x2 and 2x2 4s and s
• 6 and 2
• Unlike terms 3s and s2 2x and 5
• 3d2 and 7

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Simplify this tile model.
Write the polynomial that the remaining tiles
represent.
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To simplify

• First, we group like tiles.
• Identify and remove the zero pairs.
• The tiles that remain are
• They represent x2 x - 2

When there is only 1 of a type of tile, we omit
the coefficient 1.
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• We can also simplify a polynomial by adding the
  coefficients of the like terms. This is called
  combining like terms.
• -x2 3x2
• -1x2 3x2 2x2
• A polynomial in simplified form is a
  polynomial in which all the like terms have been
  combined.

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Simplify each polynomial.

• 5d 2 3d 1
• 5d 3d 2 1
• 8d 1
• 2a2 3a 5a2 7a
• 2a2 5a2 3a 7a
• 7a2 4a

Remember Group the like terms. Add the
coefficients of the like terms , or combine them.
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A polynomial may contain more than one variable.

• Example 4xy y2 3x2 2xy x 3y2
• We follow the same process. Group the like terms,
  (the variables must be the same letters to be
  like terms).
• 4xy 2xy y2 3y2 3x2 x
• 6xy 4y2 3x2 - x

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Polynomials can represent situations.

• Write a polynomial that represents the perimeter
  and area of each rectangle.

? 3x ?
x
x
1
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Assignment

• Pg. 222 4, 5, 8, 9, 11 ace, 18a, 12ace, 13ace,
  14ace, 22