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Algebra

Algebra. 10.3 Special Products of Polynomials. Multiply. We can find a shortcut. (x + y) (x – y). This is the sum and difference pattern. x². xy. xy. y 2. -. +. -. Shortcut: Square the first term and subtract the square of the second term. = x² - y 2.

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Algebra

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  1. Algebra 10.3 Special Products of Polynomials

  2. Multiply. We can find a shortcut. (x + y) (x – y) This is the sum and difference pattern. x² xy xy y2 - + - Shortcut: Square the first term and subtract the square of the second term. = x² - y2 This is a “DTS,” the difference of two squares.

  3. Multiply. Use the shortcut. (3x + 8y) (3x – 8y) Shortcut: Square the first term and subtract the square of the second term. = (3x)² - (8y)2 = 9x² - 64y2

  4. Try these! x²- 49 (x + 7) (x – 7) 16t²- 1 (4t + 1)(4t – 1) (9x – 5y)(9x + 5y) 81x²- 25y² (-3x + 5)(-3x – 5) 9x²- 25

  5. Multiply. We can find a shortcut. (x + y)2 This is the square of a binomial pattern. (x + y) (x + y) x² xy xy y2 + + + Shortcut: Square the first term, add twice the product of both terms and add the square of the second term. = x² + 2xy + y2 This is a “Perfect Square Trinomial.”

  6. Multiply. Use the shortcut. (4x + 5)2 x² + 2xy + y2 Shortcut: = (4x)² + 2(4x●5) + (5)2 = 16x² + 40x + 25

  7. Try these! x² + 6x + 9 (x + 3)2 25m² + 80m + 64 (5m + 8)2 (2x + 4y)2 4x² + 16xy + 16y² (-4x + 7)2 16x²- 56x + 49

  8. Multiply. We can find a shortcut. (x – y)2 This is the square of a binomial pattern. (x – y) (x – y) x² xy xy y2 - - + = x² - 2xy + y2 This is a “Perfect Square Trinomial.”

  9. Multiply. Use the shortcut. (3x - 7)2 x² - 2xy + y2 Shortcut: = 9x² - 42x + 49

  10. Try these! x² - 14x + 49 (x – 7)2 9p² - 24p + 16 (3p - 4)2 (4x - 6y)2 16x² - 48xy + 36y²

  11. A mixture of all three! 4x² + 12x + 9 (2x + 3)2 4p² - 16 (2p - 4) (2p + 4) (2x - y)2 4x² - 4xy + y²

  12. HW • P. 593-595 (15-42, 63-68)

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