Subtract 8x 5 from 5x 3x 2 Remember The subtraction operation is neither

Subtract 8x 5 from 5x 3x 2 remember the subtraction

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Subtract 8x 5 from 5x + 3x 2 Remember The subtraction operation is neither commutative nor associative . The order of the subtracted terms and the order in which the operations are performed is important . It is not commutative because 5 - 3 ≠ 3 - 5 It is not associative because (3 - 5) - 7 ≠ 3 - (5 - 7) 34
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4.4: Addition and Subtraction of Polynomials Examples: Using the Vertical Method 1. Add 3x 5 and x 2 + 2x + 4 2. Add 2x 2 5x, 3x 2 + 2 and 6x 3 3. Subtract 5x 3 from 8x 7 4. Subtract 5x 2 3 x + 4 from 8x 2 + 5x 3 35
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4.5: Multiplication of Polynomials and Special Products Objectives: 4.5.1: Find the product of a monomial and a polynomial 4.5.2: Find the product of two binomials 4.5.3: Square a binomial 4.5.4: Find the product of two binomials that differ only in sign 36
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4.5: To Multiply Monomials Example: 1. Multiply 3x 2 y and 2x 3 y 5 Remember: The multiplication operation is commutative and associative . The order of the multiplied terms and the order in which the operations are performed is not important . It is commutative because (2)(3) = (3)(2) = 6 It is associative because ((2) (3))(4) = (2)((3)(4)) = 24 37
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4.5.1: Find the Product of a Monomial and a Polynomial Example: 1. Multiply 2x + 3 by x 2. Multiply 2a 3 + 4a by 3a 2 3. 3x(4x 3 + x 2 + 2) 4. 5 c(4c 2 8c) 5. 3c 2 d 2 (7cd 2 5c 2 d 3 ) 6. 3x 2 y and 2x 3 y 5 38
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4.5.2: Find the Product of Two Binomials Example: 1. Multiply x + 2 by x + 3 2. Multiply a 3 by a 4 39
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4.5.2: Find the Product of Two Binomials Using FOIL Method Example: Multiply (x + 2) by (x + 3) 40
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4.5.2: Find the Product of Two Binomials Using FOIL Method Examples: 1. Multiply (x + 4) by (x + 5) 2. Multiply (x 7) by (x + 3) 3. Multiply (4x 3) by (3x + 2) 4. Multiply (3x 5y) by (2x 5y) 41
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4.5.2: Find the Product of Two Binomials Examples: Using the Vertical Method for Polynomials with Three or More Terms 1. Multiply (x 2 5x + 8) by (x + 3) 42
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4.5.3: Square a Binomial Squaring a binomial always results in three terms. Examples: (x + y) 2 = (x + y)(x + y) = x 2 + xy + xy + y 2 = x 2 + 2xy + y 2 (x y) 2 = (x y)(x y) = x 2 xy xy + y 2 = x 2 2xy + y 2 To Square a Binomial 43
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4.5.3: Square a Binomial Examples: 1. (x + 3) 2 2. (3a + 4b) 2 3. (y 5) 2 4. (5c 3d) 2 Note: (y + 4) 2 y 2 + 4 2 or y 2 + 16 To Square a Binomial 44
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4.5.4: Find the Product of Two Binomials that Differ Only in Sign Example: (x + y)(x y) = x 2 xy + xy y 2 = x 2 y 2 Examples: 1.
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