Special products and factoring

• Fortunately, there are some instances when multiplying polynomials becomes easier and more convenient, thanks to different techniques developed by some mathematicians. The result we obtain when multiplying polynomials under special circumstances is called special products.
• Special Cases Resulting in Special Products

  • Multiplying a binomial by another binomial (FOIL method)
  • Squaring a binomial (multiplying a binomial by itself)
  • Difference of two squares (multiplying binomials with the same terms but with opposite signs)
  • Cubing a binomial (multiplying a binomial by itself thrice)
• FOIL stands for First Terms, Outer Terms, Inner Terms, and Last Terms. The FOIL method is a technique used to multiply two binomials.
• How To Square a Binomial in 4 Steps

  1. Square the first term of the binomial.
  2. Multiply the first and second term of the binomial then multiply the product by 2.
  3. Square the last term of the binomial.
  4. Combine the results you have obtained from Step 1 to Step 3.
• special product example

  A) 4w2-12w+9

  
• For instance, if we multiply (x + y) by (x – y), we will obtain a difference of two squares since (x + y) and (x – y) have the same terms (which are x and y) but opposite signs.
• Since the binomials have the same terms but with opposite signs, we can conclude that the result will be a difference of two squares.
• Whereas the square of a binomial is the product obtained when we multiply a binomial by itself, a cube of a binomial is what you get when you multiply the same binomial by itself three times.
• examples of difference of two square

  A) 1-9p2

  
• example of combines squaring a binomial and difference of two squares

  A) x2+2xy+y2-4

  
• expand (2a-b)^3

  A) 8a3-12a2b+6ab2-b3

  
• Factoring is determining the factors of a certain expression or polynomial. We can consider factoring as the reverse process of multiplying polynomials. 
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