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(2a-3)^2

2 min read Jun 16, 2024
(2a-3)^2

Understanding the Expansion of (2a - 3)^2

The expression (2a - 3)^2 represents the square of the binomial (2a - 3). To understand its expansion, we need to apply the concept of squaring a binomial.

The FOIL Method

The FOIL method is a handy acronym that helps us remember the steps involved in expanding a binomial squared:

  • First: Multiply the first terms of each binomial.
  • Outer: Multiply the outer terms of the binomials.
  • Inner: Multiply the inner terms of the binomials.
  • Last: Multiply the last terms of each binomial.

Applying FOIL to (2a - 3)^2

Let's apply the FOIL method to expand (2a - 3)^2:

  1. First: (2a) * (2a) = 4a^2
  2. Outer: (2a) * (-3) = -6a
  3. Inner: (-3) * (2a) = -6a
  4. Last: (-3) * (-3) = 9

Now, combine the terms:

4a^2 - 6a - 6a + 9

Finally, simplify by combining like terms:

4a^2 - 12a + 9

Conclusion

Therefore, the expansion of (2a - 3)^2 is 4a^2 - 12a + 9. This is a trinomial, which is a polynomial with three terms.

Understanding the FOIL method allows us to effectively expand and simplify expressions like this, making it easier to work with them in various mathematical contexts.

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