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Lesson 1 (Simplifying Expressions)

Lesson 1 (Simplifying Expressions). What are the different properties that can help simplify expressions? Commutative Property. Commutative Associative Distributive These only work with addition and multiplication Numbers/variables can be moved around in any order. 5+7+3 = 3+7+5

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Lesson 1 (Simplifying Expressions)

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  1. Lesson 1 (Simplifying Expressions) • What are the different properties that can help simplify expressions? • Commutative Property • Commutative • Associative • Distributive • These only work with addition and multiplication • Numbers/variables can be moved around in any order. • 5+7+3 = 3+7+5 • 9y(5) = 5(9y) • 8r2 t = 8tr2

  2. Lesson 1 (Simplifying Expressions) • Associative Property • Distributive Property • Numbers can be grouped differently. • (5+7x)+6x = 5+(7x+6x) • 3w(w) = 3(w*w) • Remove parentheses by multiplying everything on the inside by the outside term.

  3. Lesson 1 (Simplifying Expressions) • Examples • Watch negative signs • 5(4x+2) • -3(4+5y) • 2x(3x-8) • -8y(3y-2)

  4. Lesson 1 (Simplifying Expressions) • How do you simplify expressions? • Distribute first to get rid of any parentheses. Combine like terms by adding or subtracting. • When adding/subtracting, you can only combine like terms. If they do not have the exact same variable, they cannot be combined. Just add/subtract numbers in front, variable stays the same. • When multiplying, any variable can be multiplied. Multiply the coefficients, add exponents on variables.

  5. Lesson 1 (Simplifying Expressions) • Examples • 2y+4x+8y • 6x+2(2x+7) • 4a3+ 6a+3a3+8a • 4(3n+9)+5n

  6. Lesson 1 (Simplifying Expressions) • Examples • (a+2b)3-3a • 5(m-7)-3m • 4(2x-1)+10(x-5) • 10-2(4x-3)

  7. Lesson 1 (Simplifying Expressions) • How do you multiply binomials? • What is the FOIL method? • Two methods: FOIL, Magic Box • Order to multiply terms: First, Outer, Inner, Last • Think of as double distributing.

  8. Lesson 1 (Simplifying Expressions) • Examples using FOIL • (x+3)(x+8) • (2x+8)(4x+3) • (3y-3)(2y+9) • (7w-4)(w-6)

  9. Lesson 1 (Simplifying Expressions) • How do you multiply using the magic box? • (x+5)(2x+3) • Make a box using terms that are being multiplied. x + 5 2x + 3

  10. Lesson 1 (Simplifying Expressions) • Examples using Magic Box • (x-5)(x+7) • (2y+3)(6y-7) • (4a-5)(3a+2) • (7y-4)(5y-1)

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