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Learn how to simplify complex algebraic expressions using neutral pairs to cancel out terms efficiently. Practice examples and visualize the process step by step.
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Remember: + + “Neutral Pairs” +
Introduction: 1 1 x x 1 1 1 x Area = 1 1 = 1 square unit Area = 1 x = x square units x2 x2 x x Area = x x = x2 square units
1 Example 1: Simplify. (5x2 + 2x – 5) + (-2x2 + 3x + 1) = 3x2 + 5x 4 Visualize. -1 x2 x2 x2 x2 x2 x -1 -1 x -1 -1 x - x2 - x2 x x Look for neutral pairs to cancel
Remember: (don't copy in notes) 2 7 = 2 +-7= -5 + +
1 1 1 1 1 1 Example 2: Simplify. (-2x2 + x – 5) (-3x2 + 5x 6) 1 = (-2x2 + x – 5) +1(+3x2 5x + 6) Visualize. = x2 – 4x + 1 -1 - x2 - x2 -1 -1 x -1 -1 - x x2 x2 x2 x2 - x - x - x - x Look for neutral pairs to cancel