5.2 Like and Unlike Terms

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.

Write the integer modeled by each set of tiles. = ________ = ________ +2 -3

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

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

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”.

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.

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.

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

Polynomials can represent situations. Write a polynomial that represents the perimeter and area of each rectangle.  3x  x x 1

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