**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:

a ^{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}