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(2x-y)^2 Expand

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

Expanding (2x - y)^2

The expression (2x - y)^2 represents the square of a binomial. To expand it, we can apply the following steps:

Understanding the Concept

The square of a binomial means multiplying the binomial by itself. So, (2x - y)^2 is equivalent to (2x - y) * (2x - y).

Applying the FOIL Method

We can use the FOIL method to expand the expression:

  • First: Multiply the first terms of each binomial: (2x) * (2x) = 4x^2
  • Outer: Multiply the outer terms of each binomial: (2x) * (-y) = -2xy
  • Inner: Multiply the inner terms of each binomial: (-y) * (2x) = -2xy
  • Last: Multiply the last terms of each binomial: (-y) * (-y) = y^2

Combining Like Terms

After applying FOIL, we get: 4x^2 - 2xy - 2xy + y^2

Combining the like terms, we get the final expanded form:

4x^2 - 4xy + y^2

Summary

Therefore, the expansion of (2x - y)^2 is 4x^2 - 4xy + y^2. This expansion can be used in various algebraic manipulations and solving equations.

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