Quadratic Expansions

Quadratic Expansions

1. Two brackets

   • (x+2)(x-5)= x2-5x+2x-10
     • = x2-3x-10
   • (x+7)(x+2)
     • = x2+2x+7x+14
       • = x2+9x+14

2. Three Brackets

   • (x+1)(x+2)(x-3)=(x+1)[(x2-x-6)]
     • = x3-x2-6x+x2-x-6
       • = x3-7x-6
   • (x+2)(x+5)(x+3)
     • = (x+2)[(x2+8x+15)
       • = x3+8x2+15x+2x2+16x+30
         • = x3+10x2+31x+30

3. Perfect Squares

   • (x+4)2
     • = (x+4)(x+4)
       • = x2+8x+16
   • (x+2)2
     • = (x+2)(x+2)
       • x2+4x+4

4. Difference between two squares

   • (x+5)(x-5)
     • = x2+5x-5x-25
       • = x2-25
   • (x+3)(x-3)
     • = x2+3x-3x-9
       • = x2-9