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(2x-3)(2x-3) Expand

2 min read Jun 16, 2024
(2x-3)(2x-3) Expand

Expanding (2x - 3)(2x - 3)

This expression represents the product of two binomials: (2x - 3) and (2x - 3). Expanding it means multiplying these binomials to get a simplified polynomial. There are two main methods to achieve this:

1. FOIL Method

FOIL stands for First, Outer, Inner, Last. This method helps us systematically multiply the terms in the binomials:

  1. First: Multiply the first terms of each binomial: (2x) * (2x) = 4x²
  2. Outer: Multiply the outer terms of the binomials: (2x) * (-3) = -6x
  3. Inner: Multiply the inner terms of the binomials: (-3) * (2x) = -6x
  4. Last: Multiply the last terms of each binomial: (-3) * (-3) = 9

Now, add all the terms together: 4x² - 6x - 6x + 9

Finally, combine the like terms: 4x² - 12x + 9

2. Distributive Property

The distributive property states that multiplying a sum by a number is the same as multiplying each term of the sum by that number. We can use it twice to expand our expression:

  1. First distribution:

    • (2x - 3) * (2x - 3) = (2x * (2x - 3)) + (-3 * (2x - 3))

  2. Second distribution:

    • (2x * (2x - 3)) + (-3 * (2x - 3)) = (4x² - 6x) + (-6x + 9)

  3. Combine like terms:

    • (4x² - 6x) + (-6x + 9) = 4x² - 12x + 9

Conclusion

Both methods result in the same expanded form: 4x² - 12x + 9. The FOIL method is a handy shortcut specifically designed for binomial multiplication, while the distributive property is a more general principle applicable to any number of terms. Choose the method you find most comfortable and efficient.

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