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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. - PowerPoint PPT Presentation
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Algebra
10.3 Special Products of Polynomials
Multiply. We can find a shortcut.
(x + y) (x – y)
x² - xy + xy - y2
= x² - y2Shortcut: 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.
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 - 64y2
Try these!
(x + 7) (x – 7)
(4t + 1)(4t – 1)
(9x – 5y)(9x + 5y)
(-3x + 5)(-3x – 5)
x²- 49
16t²- 1
81x²- 25y²
9x²- 25
Multiply. We can find a shortcut.
(x + y) (x + y)
x² + xy + xy + y2
= x² + 2xy + y2Shortcut: Square the first term, add twicethe 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.
Multiply. Use the shortcut.
(4x + 5)2
= (4x)² + 2(4x●5) + (5)2
Shortcut:
= 16x² + 40x + 25
x² + 2xy + y2
Try these!
(x + 3)2
(5m + 8)2
(2x + 4y)2
(-4x + 7)2
x² + 6x + 9
25m² + 80m + 64
4x² + 16xy + 16y²
16x²- 56x + 49
Multiply. We can find a shortcut.
(x – y) (x – y)
x² - xy - xy + y2
= x² - 2xy + y2
This is a “Perfect Square Trinomial.”
(x – y)2
This is the square of a binomial pattern.
Multiply. Use the shortcut.
(3x - 7)2
Shortcut:
= 9x² - 42x + 49
x² - 2xy + y2
Try these!
(x – 7)2
(3p - 4)2
(4x - 6y)2
x² - 14x + 49
9p² - 24p + 16
16x² - 48xy + 36y²
A mixture of all three!
(2x + 3)2
(2p - 4) (2p + 4)
(2x - y)2
4x² + 12x + 9
4p² - 16
4x² - 4xy + y²
HW
• P. 593-595 (15-42, 63-68)