(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: (12x^3y^2 - 15x^2y^3) ÷ (-3x^2y^2)

This problem involves simplifying a polynomial expression by division. Here's how to break it down:

Understanding the Problem

We're tasked with dividing the polynomial (12x^3y^2 - 15x^2y^3) by the monomial (-3x^2y^2).

Applying the Division Process

  1. Separate the terms: We can rewrite the problem as two separate divisions:

    • (12x^3y^2) ÷ (-3x^2y^2)
    • (-15x^2y^3) ÷ (-3x^2y^2)
  2. Divide the coefficients:

    • 12 ÷ (-3) = -4
    • -15 ÷ (-3) = 5
  3. Divide the variables: For each variable, subtract the exponents in the denominator from the exponents in the numerator.

    • x^3 ÷ x^2 = x^(3-2) = x
    • y^2 ÷ y^2 = y^(2-2) = y^0 = 1
    • x^2 ÷ x^2 = x^(2-2) = x^0 = 1
    • y^3 ÷ y^2 = y^(3-2) = y
  4. Combine the results:

    • (12x^3y^2) ÷ (-3x^2y^2) = -4x
    • (-15x^2y^3) ÷ (-3x^2y^2) = 5y
  5. Combine the simplified terms:

    • (-4x) + (5y)

Final Result

Therefore, the simplified expression of (12x^3y^2 - 15x^2y^3) ÷ (-3x^2y^2) is -4x + 5y.

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