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Algebra 10.3 Special Products of Polynomials

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Multiply. We can find a shortcut. (x + y) (x – y) x² - xy + - y2y2 = x² - y 2 Shortcut: Square the first term and subtract the square of the second term. This is a “DTS,” the difference of two squares. This is the sum and difference pattern.

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

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

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Multiply. We can find a shortcut. (x + y) x² + xy + + y2y2 = x² + 2xy + y 2 Shortcut: Square the first term, add twice the product of both terms and add the square of the second term. This is a “Perfect Square Trinomial.” (x + y) 2 This is the square of a binomial pattern.

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

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

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Multiply. We can find a shortcut. (x – y) x² - xy - + y2y2 = x² - 2xy + y 2 This is a “Perfect Square Trinomial.” (x – y) 2 This is the square of a binomial pattern.

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

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

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

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HW P. 593-595 (15-42, 63-68)

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