%5E2.jpeg "(3a-2)^2")
Expanding (3a - 2)^2
The expression (3a - 2)^2 is a perfect square trinomial. It's important to understand how to expand this expression correctly, as it's a fundamental concept in algebra.
Understanding the Concept
The expression (3a - 2)^2 is equivalent to multiplying (3a - 2) by itself:
(3a - 2)^2 = (3a - 2)(3a - 2)
Expanding the Expression
To expand this, we can use the FOIL method (First, Outer, Inner, Last):
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First: Multiply the first terms of each binomial: (3a) * (3a) = 9a^2
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Outer: Multiply the outer terms of each binomial: (3a) * (-2) = -6a
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Inner: Multiply the inner terms of each binomial: (-2) * (3a) = -6a
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Last: Multiply the last terms of each binomial: (-2) * (-2) = 4
Now, combine the like terms:
9a^2 - 6a - 6a + 4 = 9a^2 - 12a + 4
The Result
Therefore, the expanded form of (3a - 2)^2 is 9a^2 - 12a + 4.
Key Takeaways
- Perfect Square Trinomials: Remember that (a - b)^2 is always equal to a^2 - 2ab + b^2.
- FOIL Method: Use the FOIL method for expanding binomials.
- Combining Like Terms: Always simplify the expression by combining like terms.