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FOIL Method: Expanding (x+y)(x-y)
In algebra, expanding the product of two binomials is a crucial skill to master. One of the most common types of binomial products is (x+y)(x-y). In this article, we will explore how to expand this product using the FOIL method.
What is the FOIL Method?
The FOIL method is a technique used to expand the product of two binomials. FOIL stands for "First, Outer, Inner, Last," which refers to the order in which you multiply the terms.
Expanding (x+y)(x-y) using FOIL
To expand (x+y)(x-y), we will follow the FOIL method:
Multiply the First terms
The first terms are x and x. Multiply them together:
x × x = x^2
Multiply the Outer terms
The outer terms are x and -y. Multiply them together:
x × -y = -xy
Multiply the Inner terms
The inner terms are y and x. Multiply them together:
y × x = xy
Multiply the Last terms
The last terms are y and -y. Multiply them together:
y × -y = -y^2
Combine like terms
Now, combine the results of the FOIL method:
x^2 - xy + xy - y^2
Simplify the expression
Notice that the -xy and xy terms cancel each other out:
x^2 - y^2
And that's the final answer! The expanded form of (x+y)(x-y) is x^2 - y^2.
Conclusion
In this article, we learned how to expand the product of (x+y)(x-y) using the FOIL method. By following the steps of the FOIL method, we were able to arrive at the final answer of x^2 - y^2. This skill is essential in algebra and will be useful in a variety of mathematical applications.
