Section 5 2 Simplifying Like Unlike Terms p

Section 5. 2 – Simplifying (Like & Unlike Terms) p. ______

Like Terms = terms that can be represented by algebra tiles with the same size & shape • Exponent on the variable will be the same • Tile colour can be different! ex) -2 x 2 and x 2 are like terms ex) 4 x, -x, and -2 x are like terms

Unlike terms are modeled with different algebra tiles ex) -3 x 2 and 2 x are unlike terms

Simplifying Polynomials A simplified polynomial will: • use the fewest tiles possible • Have a symbolic form containing only one term of each degree To simplify: 1. Group like terms 2. Remove zero pairs 3. Combine like terms

ex) Simplify: 3 n 2 + 4 – x + 2 x – 4 n 2 + 1 1. Group (in descending order!) 2. Remove zero pairs

3. Combine like terms What’s left? -n 2 + x + 5 Try without using algebra tiles (symbolically): ex) 4 x 2 + 2 – 7 x + 5 x – 6 x 2 + 1 – x 4 x 2 – 6 x 2 – 7 x + 5 x – x + 2 + 1 - 2 x 2 – 3 x +3 reorder Gather like terms

Perimeter Questions: 1. Write a polynomial to represent the perimeter: x x x x x 1 x x P=x+x+x+x+x+x P = 10 x P=x+1+1+1+x+1+1+1 P = 2 x + 6

Simplifying Polynomials with 2 Variables ex) 2 xy – 3 x 2 + y 2 + 2 xy – 2 x 2 – 4 y 2 -3 x 2 – 2 x 2 + 2 xy + y 2 – 4 y 2 - 5 x 2 + 4 xy – 3 y 2 p. ______ # reorder Gather like terms