(12x^3y^2-15x^2y^3)÷(-3x^2y^2)

2 min read Jun 16, 2024

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:

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

Separate the terms: We can rewrite the problem as two separate divisions:
- (12x^3y^2) ÷ (-3x^2y^2)
- (-15x^2y^3) ÷ (-3x^2y^2)
Divide the coefficients:
- 12 ÷ (-3) = -4
- -15 ÷ (-3) = 5
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
Combine the results:
- (12x^3y^2) ÷ (-3x^2y^2) = -4x
- (-15x^2y^3) ÷ (-3x^2y^2) = 5y
Combine the simplified terms:
- (-4x) + (5y)

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