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(12x^3y^2-15x^2y^3)/(-3x^2y^2)

2 min read Jun 16, 2024
(12x^3y^2-15x^2y^3)/(-3x^2y^2)

Simplifying the Expression (12x³y² - 15x²y³)/(-3x²y²)

This article will guide you through the process of simplifying the algebraic expression (12x³y² - 15x²y³)/(-3x²y²).

Understanding the Expression

The expression represents a division of two terms:

  • Numerator: 12x³y² - 15x²y³
  • Denominator: -3x²y²

Simplifying the Expression

  1. Factor out the Greatest Common Factor (GCF) from the numerator: The GCF of 12x³y² and 15x²y³ is 3x²y². Therefore, we can rewrite the numerator as:

    12x³y² - 15x²y³ = 3x²y²(4x - 5y)

  2. Rewrite the expression with the factored numerator:

    (12x³y² - 15x²y³)/(-3x²y²) = [3x²y²(4x - 5y)] / (-3x²y²)

  3. Cancel out the common factors: Notice that both the numerator and denominator share the factor 3x²y². We can cancel these out:

    [3x²y²(4x - 5y)] / (-3x²y²) = (4x - 5y) / (-1)

  4. Simplify further: Since dividing by -1 simply changes the sign of the expression:

    (4x - 5y) / (-1) = -4x + 5y

Final Result

Therefore, the simplified form of the expression (12x³y² - 15x²y³)/(-3x²y²) is -4x + 5y.

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