# Factor Trinomials with Two Variables

How to factor Trinomials with two variables?
Sometimes a trinomial may consists of two variables. We can factor the trinomial in a similar way as if it has only one variable. We can use the trial and error method (reverse FOIL method), the grouping method or the AC method.

Related Topics: Factoring Trinomials

Example:

Factor the following trinomials:
a) e26ef + 9f2
b) 2x2 + 7xy 15y2

Solution:

a) e2 6ef + 9f2 = (e 3f)2
b) 2x2 + 7xy 15y2 = (2x 3y)(x + 5y)

Factoring trinomials with two variables
Step 1: Find the Product, Sum and the two numbers that "work"
Product = (First number) &time; (Last number)
Sum = (Middle Number)
Find two numbers that when multiplied gives the Product and when added gives the Sum.
Step 2: Split the middle term.
Step 3: Group in twos and remove the GCF of each group.
Step 4: Write in factored form.

Examples:
1. 2c2 + 13cd + 6d2
2. 5x2 - 6xy + 1

How to factor trinomials with two variables and a = 1?
Some strategies to factor trinomials that have a = 1
Examples:
1. a2 - 9ab + 14b2
2. m2 - mn - 30n2
How to factor trinomial with two variables and a > 1?
Example:
18m2 - 9mn - 2n2
Factor trinomial containing two variables
Example:
v2 + 5vf - 24f2 How to factor trinomial with two variables using gcf then grouping?
Example:
6m6n + 11m5n2 + 3m4n3

How to factor a trinomial with two variables using the AC Method?
Example:
30x3y - 25x2y2 - 30xy3 How to Factor Trinomials with Two Variables using the reverse FOIL or trial and error method?
Examples:
1. 12x2 - 5xy - 2y2
2. 6x2 - 17xy + 10y2

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