Special Products Summary

Key Concepts

• Binomial Squares Pattern
  • If \(a,b\) are real numbers,
    
  • \({\left(a+b\right)}^{2}={a}^{2}+2ab+{b}^{2}\)
  • \({\left(a-b\right)}^{2}={a}^{2}-2ab+{b}^{2}\)
  • To square a binomial: square the first term, square the last term, double their product.
• Product of Conjugates Pattern
  • If \(a,b\) are real numbers,
    
  • \(\left(a-b\right)\left(a+b\right)={a}^{2}-{b}^{2}\)
  • The product is called a difference of squares.
• To multiply conjugates:
  • square the first term square the last term write it as a difference of squares