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(3x-5)^2 Expand

2 min read Jun 16, 2024
(3x-5)^2 Expand

Expanding (3x - 5)^2

The expression (3x - 5)^2 represents the square of the binomial (3x - 5). To expand this expression, we can use the FOIL method or the square of a binomial pattern.

Using the FOIL Method

FOIL stands for First, Outer, Inner, Last. This method helps us multiply each term in the first binomial with each term in the second binomial.

  1. First: Multiply the first terms of each binomial: (3x)(3x) = 9x^2
  2. Outer: Multiply the outer terms of the binomials: (3x)(-5) = -15x
  3. Inner: Multiply the inner terms of the binomials: (-5)(3x) = -15x
  4. Last: Multiply the last terms of each binomial: (-5)(-5) = 25

Now, add all the terms together: 9x^2 - 15x - 15x + 25

Finally, combine the like terms: 9x^2 - 30x + 25

Using the Square of a Binomial Pattern

The square of a binomial pattern states: (a - b)^2 = a^2 - 2ab + b^2

In our case, a = 3x and b = 5.

  1. Square the first term: (3x)^2 = 9x^2
  2. Multiply the first and second term, then double it: 2(3x)(-5) = -30x
  3. Square the second term: (5)^2 = 25

Adding these terms together, we get: 9x^2 - 30x + 25

Conclusion

Both the FOIL method and the square of a binomial pattern lead to the same expanded form of (3x - 5)^2, which is 9x^2 - 30x + 25. Choose the method that you find most comfortable and easier to apply.

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