(a-b)-answer.jpeg "(a+b)(a-b) Answer")
FOIL Method: Expanding (a+b)(a-b)
In algebra, expanding the product of two binomials is a fundamental concept. One of the most common examples is expanding the product of (a+b) and (a-b). In this article, we'll explore how to expand (a+b)(a-b) using the FOIL method.
What is the FOIL Method?
FOIL is an acronym that stands for "First, Outer, Inner, Last." It's a technique used to expand the product of two binomials by multiplying each term in one binomial with each term in the other binomial.
Expanding (a+b)(a-b)
Let's expand (a+b)(a-b) using the FOIL method:
F (First): Multiply the first terms in each binomial
(a) × (a) = a^2
O (Outer): Multiply the outer terms in each binomial
(a) × (-b) = -ab
I (Inner): Multiply the inner terms in each binomial
(b) × (a) = ab
L (Last): Multiply the last terms in each binomial
(b) × (-b) = -b^2
Now, combine the terms:
a^2 - ab + ab - b^2
Simplifying the Expression
Notice that the -ab and ab terms cancel each other out:
a^2 - b^2
And that's the final answer! The expansion of (a+b)(a-b) is indeed a^2 - b^2.
Conclusion
In this article, we learned how to expand (a+b)(a-b) using the FOIL method. By multiplying each term in one binomial with each term in the other binomial, we arrived at the simplified expression a^2 - b^2. This technique is essential in algebra and is used to expand various types of binomials.
