%5E2.jpeg "(3a-1)^2")
Expanding (3a-1)^2
The expression (3a-1)^2 represents the square of the binomial (3a-1). Expanding this expression involves applying the distributive property or using the FOIL method.
Using the Distributive Property:
The distributive property states that a(b+c) = ab + ac. We can apply this to our expression:
(3a-1)^2 = (3a-1)(3a-1)
First, we distribute the 3a:
3a(3a-1) - 1(3a-1)
Then we distribute again:
9a^2 - 3a - 3a + 1
Finally, we combine like terms:
9a^2 - 6a + 1
Using the FOIL Method:
FOIL stands for First, Outer, Inner, Last. This method helps remember the steps for multiplying two binomials:
(3a-1)(3a-1)
First: 3a * 3a = 9a^2
Outer: 3a * -1 = -3a
Inner: -1 * 3a = -3a
Last: -1 * -1 = 1
Combining the terms, we get:
9a^2 - 6a + 1
Conclusion
Whether using the distributive property or FOIL method, we arrive at the same expanded expression for (3a-1)^2: 9a^2 - 6a + 1. This expanded form can be useful for solving equations, simplifying expressions, or analyzing the behavior of the original expression.