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(3y-4)^2

2 min read Jun 16, 2024
(3y-4)^2

Expanding (3y - 4)^2

The expression (3y - 4)^2 represents the square of a binomial. To expand it, we can use the FOIL method or the pattern for squaring a binomial.

Using FOIL

FOIL stands for First, Outer, Inner, Last, which helps us remember the order to multiply the terms:

  1. First: Multiply the first terms of each binomial: (3y)(3y) = 9y^2
  2. Outer: Multiply the outer terms: (3y)(-4) = -12y
  3. Inner: Multiply the inner terms: (-4)(3y) = -12y
  4. Last: Multiply the last terms: (-4)(-4) = 16

Now, combine the terms: 9y^2 - 12y - 12y + 16

Finally, simplify by combining like terms: 9y^2 - 24y + 16

Using the Pattern

Squaring a binomial follows a pattern: (a + b)^2 = a^2 + 2ab + b^2. We can apply this pattern to our expression:

  1. Square the first term: (3y)^2 = 9y^2
  2. Multiply the two terms and double the product: 2(3y)(-4) = -24y
  3. Square the second term: (-4)^2 = 16

Combine the terms: 9y^2 - 24y + 16

Conclusion

Both methods lead to the same expanded form of (3y - 4)^2: 9y^2 - 24y + 16. Choose the method you find easier or more comfortable to use.

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