(3/4x-4/3y) (2/3x+3/2y)

Jasonbradley

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Jun 16, 2024

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Multiplying Binomials: (3/4x - 4/3y) (2/3x + 3/2y)

This article will guide you through the process of multiplying the two binomials: (3/4x - 4/3y) (2/3x + 3/2y).

Understanding the Process

Multiplying binomials involves using the distributive property twice. This essentially means multiplying each term in the first binomial by each term in the second binomial.

Step-by-Step Solution

1. Distribute the first term of the first binomial: (3/4x) * (2/3x) + (3/4x) * (3/2y)

2. Distribute the second term of the first binomial:

   • (4/3y) * (2/3x) - (4/3y) * (3/2y)

3. Simplify each term:

   • (3/4x) * (2/3x) = 1/2x²
   • (3/4x) * (3/2y) = 9/8xy
   • -(4/3y) * (2/3x) = -8/9xy
   • -(4/3y) * (3/2y) = -2y²

4. Combine like terms: 1/2x² + 9/8xy - 8/9xy - 2y²

5. Simplify the final expression: 1/2x² + 1/72xy - 2y²

Conclusion

By applying the distributive property and simplifying the resulting terms, we successfully multiplied the binomials (3/4x - 4/3y) (2/3x + 3/2y) and arrived at the final expression: 1/2x² + 1/72xy - 2y².