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(2x-3y)^2 Simplify

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

Simplifying (2x - 3y)^2

This article will guide you through the steps of simplifying the expression (2x - 3y)^2.

Understanding the Concept

The expression (2x - 3y)^2 represents the square of the binomial (2x - 3y). This means the expression is multiplied by itself.

Therefore:

(2x - 3y)^2 = (2x - 3y) * (2x - 3y)

Applying the FOIL Method

To simplify this, we can use the FOIL method, which stands for:

  • First
  • Outer
  • Inner
  • Last

This method helps us to multiply each term in the first binomial by each term in the second binomial.

Steps for Simplification

  1. Multiply the First terms: 2x * 2x = 4x^2

  2. Multiply the Outer terms: 2x * -3y = -6xy

  3. Multiply the Inner terms: -3y * 2x = -6xy

  4. Multiply the Last terms: -3y * -3y = 9y^2

  5. Combine the terms: 4x^2 - 6xy - 6xy + 9y^2

  6. Simplify by combining like terms: 4x^2 - 12xy + 9y^2

Final Result

Therefore, the simplified form of (2x - 3y)^2 is 4x^2 - 12xy + 9y^2.

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