Friday, November 19, 2010

Types of Factoring

  • Difference of two squares
    • a2- b= (a + b)(a - b)
    • (a-5)(a+5)
    • (x-10)(x-10)
    • (y-18)(y+18)
  • Trinomial perfect squares  
  •           x² + 6x + 9 = (x + 3)²
    •   x² − 4x + 4 = (x − 2)²
              x² + 10x + 25 = (x + 5)²
      • Sum of two cubes
        • a3 + b3
          • 3 - cube root 'em
          • 2 - square 'em
          • 1 - multiply and change
      Example 1: Factor x3 + 125.




      Example 2: Factor 8 x3 − 27.




      Example 3: Factor 2 x3 + 128 y3.
      First find the GFC. GFC = 2



      • Sum of two cubes
        • a3 - b3 
          • 3 - cube root 'em
          • 2 - square 'em
          • 1 - multiply and change 
            •  
            x3 − 27= (x − 3)(x2 + 3x+ 9)  

          125 − x3=(5 − x)(25 + 5x + x2)

        • 1 − a3=(1 − a)(1 + a+ a2)
        • Binomial expansion
          • (a + b)3 = Use the pattern
          • (a + b)4 = Use the pattern
          (5x - y)3 = 125x 3 -75x 2 y + 15xy 2 - y 3.
          (2x + 3y)4 =16x 4 +96x 3 y + 216x 2 y 2 +216xy 3 +81y 4



           



           
           

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