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How to Factor Perfect Binomials

A binomial is a phrase used for an algebraic equation that consists of exactly two terms. To "expand" the binomial, or find its product, you must square the binomial. In mathematical values, for example, the binomial (a + b)^2 is expanded to a^2 + 2ab + b^2. In a perfect binomial, also known as a perfect square binomial, the value squared is easily factorable since the second and third terms relate to the binomial value "b."

Instructions

- 1
  Divide the numerical value of the second term by two to obtain the value "b" for the universal trinomial equation. For example, if the perfect square expression is x^2 + 6x + 9, dividing the second term, 6, by two would give you the value 3.
- 2
  Take the square root of the third term. If the equation is a perfect binomial, the number should also the value of "b" found in the previous step. For example, if the perfect square expression is x^2 + 6x + 9, taking the square root of the third term, 9, would also give you the value of 3.
- 3
  Write the equation for the perfect square binomial with the universal equation: (a + b)^2. The letter "a" in the equation equals the value "x" while the letter "b" represents the value you found in Steps 1 and 2. For example, the expression x^2 + 6x + 9 would be factored out as (x + 3)^2.

Numerology