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Section 8.8-8.9 Day 2 Difference of Squares Perfect Square Trinomials Factor by Grouping
Algebra 1
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Example 1: GCF/Difference of Squares
Factor 27 𝑔 3 −3𝑔. Hint (Take out GCF first) 2𝑔(9 𝑔 2 −1) A=3g B=1 2𝑔(3𝑔+1)(3𝑔−1)
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Example 2: GCF/Difference of Squares
Factor 9 𝑥 3 −4𝑥. Hint: (Take out GCF first) 𝑥(9 𝑥 2 −4) A= 3x B= 2 𝑥(3𝑥+2)(3𝑥−2)
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Example 3: GCF/Difference of Squares
Solve 25 𝑑 3 −49𝑑=0 1. Factor GCF: 𝑑 25 𝑑 2 −49 =0 2. Factor Difference of Squares: 𝑑 5𝑑+7 5𝑑−7 =0 3. Solve using Zero Product Property 𝑑=0, 𝑑=− 7 5 , 𝑑= 7 5
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Example 4: GCF/Difference of Squares
Solve 9 𝑥 3 =4𝑥 1. Move to one side: 9 𝑥 3 −4𝑥=0 2. Factor GCF: 𝑥 9 𝑥 2 −4 =0 3. Factor Difference of Squares: 𝑥 3𝑥+2 3𝑥−2 =0 4. Solve using ZPP: 𝑥=0, 𝑥=− 2 3 , 𝑥= 2 3
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Example 5: Repeated Factoring
B =1 4 𝑦 2 +1 (4 𝑦 2 −1) A= 2y B= 1 (4 𝑦 2 +1)(2𝑦−1)(2𝑦−1)
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Example 6: Repeated Factoring
9− 𝑥 𝑥 2 (3−𝑥)(3+𝑥)(9+ 𝑥 2 )
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Example 7: Multiple Techniques
Factor 2 𝑚 3 + 𝑚 2 −50𝑚−25 2 𝑚 3 + 𝑚 2 +(−50𝑚−25) 𝑚 2 2𝑚+1 +−25(2𝑚+1) (2𝑚−1)( 𝑚 2 −25) (2𝑚−1)(𝑚+5)(𝑚−5)
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Example 8: Multiple Techniques
Factor 𝑥 4 +6 𝑥 3 −36 𝑥 2 −216𝑥 𝑥( 𝑥 3 +6 𝑥 2 −36𝑥−216) 𝑥[ 𝑥 3 +6 𝑥 2 + −36𝑥−216 ] 𝑥 𝑥 2 𝑥+6 +−36 𝑥+6 𝑥(𝑥+6)( 𝑥 2 −36) 𝑥(𝑥+6)(𝑥+6)(𝑥−6)
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