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Section 5.2 – Simplifying (Like & Unlike Terms)
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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) -2x2 and x2 are like terms ex) 4x, -x, and -2x are like terms
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Unlike terms are modeled with different algebra tiles ex) -3x2 and 2x are unlike terms
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Simplifying Polynomials
A simplified polynomial will: use the fewest tiles possible Have a symbolic form containing only one term of each degree To simplify: Group like terms Remove zero pairs Combine like terms
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ex) Simplify: 3n2 + 4 – x + 2x – 4n2 + 1
1. Group (in descending order!) 2. Remove zero pairs
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Try without using algebra tiles (symbolically):
3. Combine like terms What’s left? -n2 + x + 5 Try without using algebra tiles (symbolically): ex) 4x2 + 2 – 7x + 5x – 6x2 + 1 – x 4x2 – 6x2 – 7x + 5x – x - 2x – 3x reorder Gather like terms
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Perimeter Questions: 1. Write a polynomial to represent the perimeter:
x x x x P = x + x + x + x + x + x + x + x + x + x x x x x x P = 10x x P = x x x P = 2x + 6 1
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Simplifying Polynomials with 2 Variables
ex) 2xy – 3x2 + y2 + 2xy – 2x2 – 4y2 -3x2 – 2x2 + 2xy + 2xy + y2 – 4y2 - 5x2 + 4xy – 3y2 reorder Gather like terms p. ______ #
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