Mathematics

• Special products


  • Square of a binomial
  • Sum and difference of two squares
  • Square of a trinomial
  • Cube of a binomial
  • Sum or difference of two cubes
• Solving the square of a binomial

  1. Square the first term

  2. Multiply the first term and the second term times 2

  3. Square the second term
• Square of a binomial

  • a^2 + 2ab + b^2
  • 2x^2 + 4xy + y^2
  • 25m^2 - 40mn + 16n^2
• Binomial


  An expression with two terms
• Foil method


  Expand the binomial by multiplying the first, outer, inner, and last terms
• Solving the sum and difference of two squares

  1. Square the first term

  2. Subtract the square of the second term
• Sum and difference of two squares

  • x^2 - y^2
  • 25m^2 - 16n^2
  • 49a^2 - 1
• Trinomial


  An expression with three terms
• Solving the square of a trinomial

  1. Square the first term

  2. Square the second term

  3. Square the third term

  4. Multiply the first and second terms times 2

  5. Multiply the second and third terms times 2

  6. Multiply the first and third terms times 2
• Square of a trinomial

  • (2x + 3y + z)^2
  • (5m - 2n - 3p)^2
• Solving the cube of a binomial

  1. Cube the first term

  2. Square the first term and multiply by the second term times 3

  3. Square the second term and multiply by the first term times 3

  4. Cube the second term
• Exponent pattern

  The exponent on the first term decreases, the exponent on the second term increases
• Cube of a binomial


  • (2x + 1)^3
  • (3m + 4)^3
• Solving the sum or difference of two cubes

  1. Cube the first term

  2. Cube the second term
• Sum or difference of two cubes

  • (2x - 3y)(4x^2 + 6xy + 9y^2)
  • (5m + 4n)(25m^2 - 20mn + 16n^2)