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(1-2y)^2

less than a minute read Jun 16, 2024
(1-2y)^2

Expanding (1 - 2y)^2

The expression (1 - 2y)^2 represents the square of a binomial. To expand it, we can use the following methods:

Method 1: FOIL Method

  • First: 1 * 1 = 1
  • Outer: 1 * -2y = -2y
  • Inner: -2y * 1 = -2y
  • Last: -2y * -2y = 4y^2

Combining like terms, we get: 1 - 2y - 2y + 4y^2 = 1 - 4y + 4y^2

Method 2: Square of a Binomial Formula

The formula for squaring a binomial is: (a - b)^2 = a^2 - 2ab + b^2

Applying this to our expression:

  • a = 1
  • b = 2y

Substituting into the formula: 1^2 - 2(1)(2y) + (2y)^2 = 1 - 4y + 4y^2

Conclusion

Both methods result in the same expanded form of (1 - 2y)^2, which is 1 - 4y + 4y^2.

Remember, understanding how to expand binomials is crucial in algebra and other mathematical fields.

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