%5E2.jpeg "(a-6)^2")
Understanding (a - 6)^2
The expression (a - 6)^2 represents the square of the binomial (a - 6). To understand this, let's break it down step by step.
What is a binomial?
A binomial is a polynomial with two terms. In this case, our binomial is (a - 6).
What does squaring mean?
Squaring a number or expression means multiplying it by itself. So, (a - 6)^2 is the same as (a - 6) * (a - 6).
Expanding the expression
To expand (a - 6)^2, we can use the distributive property (also known as FOIL):
First: a * a = a^2 Outer: a * -6 = -6a Inner: -6 * a = -6a Last: -6 * -6 = 36
Now, we add all these terms together:
a^2 - 6a - 6a + 36
Simplifying the result
Combining the like terms, we get:
a^2 - 12a + 36
Conclusion
Therefore, the expanded form of (a - 6)^2 is a^2 - 12a + 36. This is a common algebraic expression that can be used in various mathematical problems.