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Factoring Patterns Difference of Perfect Squares 25 x 2 1 Factor out the GCF if there is one Step 2: Check whether you have difference of squares Step 3: Use difference of squares pattern to factor Step 1: a 2 b2 (a b)(a b) Practice: x2 4 x2 9 36 x 2 25 36 x 2 9 x 2 16 2 x 2 72 Sum and Difference of Cubes Perfect cubes: numbers whose factors can be written as a number times itself times itself like 64 = _______ Sum or Difference of Cubes: Use for two terms that are perfect cubes with a ________ or __________ sign between the terms. Sum of cubes: a3 + b3 = x3 + 27 = _________________________ Difference of cubes: a3 – b3 = _________________________ 64a3 – 27= Always look for a ______________________________, ______ first! Check the ______________________ next to see if you can factor any further. PRACTICE: Factor the following polynomials. -54x3 + 150 10x 4 – 80x 2x4 + 3x3 + 2x + 3 Perfect Square Trinomials Perfect square trinomials have the following pattern: 1x2 + 2x + 1 a2 + 2ab + b2 = (a + b)(a + b) = _____________ a2 - 2ab + b2 = (a - b)(a - b) = _____________ 4x2 – 12x + 9 You can factor them by grouping, but knowing the pattern makes the factoring easier. **Remember to take out the _____________________________ first! a) x2 - 8x + 16 b) 9y2 + 60y + 100 a)________________________ c) 2y4 + 20y2 + 50 b)_________________________ d) 2x2 - 12xy + 18y2 c)________________________ d)_________________________ Additional Practice: Factor completely x5- x3 + 8x2- 8