Factoring With Two Variables
Understand factoring with two variables in Grade 9 math — Explanation Don't panic when you see a second variable! Part of Advanced Factoring and Functions for Grade 9.
Key Concepts
Property When factoring a trinomial with two variables, like $ax^2 + bxy + cy^2$, one variable should descend in power while the other ascends. Explanation Don't panic when you see a second variable! Just treat it like a sidekick. Factor the numbers like normal, then attach the second variable to the last term of each binomial. The FOIL method will work just the same. Examples $2x^2 11xy + 5y^2 = (2x y)(x 5y)$ because the middle term is $ 10xy xy = 11xy$. $6x^2 + 7xy + 2y^2 = (2x+y)(3x+2y)$ because the middle term is $4xy + 3xy = 7xy$.
Common Questions
What is 'Factoring With Two Variables' in Grade 9 math?
Explanation Don't panic when you see a second variable! Factor the numbers like normal, then attach the second variable to the last term of each binomial.
How do you solve problems involving 'Factoring With Two Variables'?
Factor the numbers like normal, then attach the second variable to the last term of each binomial. $6x^2 + 7xy + 2y^2 = (2x+y)(3x+2y)$ because the middle term is $4xy + 3xy = 7xy$.
Why is 'Factoring With Two Variables' an important Grade 9 math skill?
Common mistake tip: A common mistake is forgetting to add the second variable (`q` in our example) back into the final answer.. Always remember that if the original problem has two variables, your factored answer must also have two variables!.