Factoring
Factoring
Perfect Square Trinomials
Sometimes the trinomial that needs to be factored is a perfect square trinomial. A perfect square trinomial is a trinomial that can be written so that its first term is the square of some quantity a, its last term is the square of some quantity b, and its middle term is twice the product of the quantities a and b. There are special formulas that can be used to factor these perfect square trinomials:
a2 + 2ab + b2 = (a + b)2
a2 - 2ab + b2 = (a - b)2
Example 1 Factor x2 + 10x + 25
Step 1. Determine if the first and last terms are perfect squares.
The first term is x2, which is (x)2 - yes.
The last term is 25, which is (5)2 - yes.
Step 2. Determine if the middle term fits the pattern 2ab.
a = 1 and b = 5
The middle term is 10x, which is 2 (5)(1)x - yes.
Step 3. Substitute values for a and b into the formula.
.