This document provides a summary of factoring techniques including: 1) Squaring binomials using the formula (a + b)2 = a2 + 2ab + b2 and (a - b)2 = a2 - 2ab + b2. 2) Factoring the difference of squares using the formula (a2 - b2) = (a + b)(a - b). 3) Factoring trinomials that are the product of a sum and difference using the formulas a2 - b2 = (a + b)(a - b). 4) Expanding cubes using the formula (x + a)3 = x3 + 3x2a +

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3. Review Factoring Trinomials
Factor the following:
c) 3x2 ­ 5x ­12 d) ­2x2 + 11x ­5
e) 2x2 ­ 6 x +4
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6. Assignment from yesterday
Check your copies to be sure you can read the following
questions:
31. 4x2 ­ 18x ­ 10
33. 3t4 + 9t2 +4t
35. 12r2 + 27r +15
37. 6 + 5y ­ 4y2 41. 6m2 + mn ­ 2 n2
39. 12 + 18t + 8t2 43. 10a2 ­ 3ab ­ b2
45. 6c2 + 13cd +2d2
47. 6x2 ­ 9xy + 3y2
49. 4y2 + 4xy ­ 8x2
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7. Special Products and Special Quadratics
Squaring binomials
Product of a sum and difference
Cube of a Binomial
Difference of squares
Perfect Squares
Difference of squares
Difference of cubes
Sum of cubes
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8. Squaring Binomials
(a + b)2 = a2 + 2ab + b2
Perfect Square Trinomial
2 2 2
(a ­ b) = a ­ 2ab + b
Example 1
Expand (3x +2y )2
Example 2
Expand (3x ­ y )2
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9. Difference of Squares­ A polynomial of the form ( a2 ­ b2). The factors of
the difference of squares are ( a2 ­ b2) = (a + b)( a ­ b)
Example 3
Factor x2 ­ 25
Example 4
Factor 9x2 ­ 16
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10. Example 5 Removing a common factor
8x2 ­ 18y2
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11. Example 6
Is 4x2 + 20x + 25 a perfect square?
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12. Product of a sum and a difference
a2 ­ b2 = (a + b)( a ­ b)
Example 7
( 4x + 3y)(4x ­ 3y)
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13. Cube of a Polynomial
Example 8
(x + 3 )3
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14. Assignment
page 133 questions 1 ­12
page 112 questions 1­4, 17 ­ 23 (odd), 31 ­42 (odd)
page 141 questions 94
Quiz on Friday.
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