Special Products

• Square of Binomials:

  1.) Square the first term

  2.) Multiply the 1st and 2nd term, multiply the product by two

  3.) Square the last or second term

  
  

  (x + y)2 = x2 + 2xy + y2

  (x - y)2 = x2 - 2xy + y2
• Cube of Binomial:

  1.) Cube the first term

  2.) Square the 1st term multiplied by the 2nd term, times 3

  3.) Square the 2nd term multiplied by the 1st term, times 3

  4.) Cube the last or second term

  
  

  Ex: (x + 3)3

  = (x)3 + 3(x)2(3) + 3(x)(3)2 + (3)3

  = x3 + 9x2 + 27x + 27
• Square of Trinomial:

  1.) Square each term

  2.) Multiply the 1st and 2nd term, times two

  3.) Multiply the 1st and 3rd term, times two

  4.) Multiply the 2nd and 3rd term, times two

  Ex: (x + y + z)2

  = x2 + y2 + z2 + 2xy + 2xz + 2yz
• Sum & Difference of TWO terms

  1.) Multiply the 1st terms

  2.) Multiply the 2nd terms

  Ex: (a + b)(a - b)

  = a2 - b2
• Special Case of multiplying Binomial and Trinomial

  1.) Multiply the 1st terms

  2.) Multiply the last terms

  
  

  Ex: (a + b)(a2 - ab + b2)

  = a3 + b3

  
  

  Note: The first and last term of the trinomial, is the square of the first and last term of the binomial. The middle term of the trinomial is the product of the two terms of the binomial