(3a-2)^2

2 min read Jun 16, 2024
(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):

  1. First: Multiply the first terms of each binomial: (3a) * (3a) = 9a^2

  2. Outer: Multiply the outer terms of each binomial: (3a) * (-2) = -6a

  3. Inner: Multiply the inner terms of each binomial: (-2) * (3a) = -6a

  4. 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.

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