Perfect square trinomial

Perfect square trinomial (for TCP brevity). It is a three-term polynomial that results from squaring a binomial.

Summary

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  • 1 Example
  • 2 Rule to know if a trinomial is a perfect square
  • 3 Procedure for factoring (+)
  • 4 Procedure for factoring (-)
  • 5 Sources

Example

Every trinomial of the form: a 2 + 2ab + b 2 is a perfect square trinomial since (a + b) 2 = (a + b) (a + b) = a 2 + ab + ab + b 2 Being the rule : The square of the first plus twice the first for the second term plus the square of the second term.

Rule to know if a trinomial is a perfect square

  • An ordered trinomial in relation to a letter.
  • It is a perfect square when the first and third terms are perfect squares.
  • The second term is the double product of its square roots.

Procedure for factoring (+)

  • The square root of the first and third terms is extracted; in example a and b.
  • A product of two binomial factors is formed with the sum of these roots; then (a + b) (a + b).
  • This product is the factored expression (a + b) 2.

If the exercise were like this:

2 – 2ab + b 2 = (a – b) 2

Procedure for factoring (-)

  • The square root of the first and third terms is extracted; in example a and b.
  • A product of two binomial factors is formed with the difference of these roots; so.

(a – b) (a – b).

  • This product is the factored expression (a – b) 2.

Example 1 Factor x 2 + 10x + 25 The square root of: x 2 is x The square root of: 25 is 5 The double product of the roots: 2 (x) (5) is 10x Then x 2 + 10x + 25 = (x + 5) 2

Example 2 Factor 49y 2 + 14y + 1 The square root of: 49y 2 is 7y The square root of: 1 is 1 The double product of the roots: 2 (7y) (1) is 14y Then 49y 2 + 14y + 1 = (7y + 1) 2

Example 3 Factor 81z 2 – 180z + 100 The square root of: 81z 2 is 9z The cube root of: 100 is 10 The double product of the roots: 2 (9z) (10) is 180z Then 81z 2 – 180z + 100 = (9z – 10) 2

 

 

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