(1/5x+2y)(2/3x-y)

2 min read Jun 16, 2024
(1/5x+2y)(2/3x-y)

Expanding the Expression: (1/5x + 2y)(2/3x - y)

This article will walk you through the process of expanding the expression (1/5x + 2y)(2/3x - y).

Understanding the Problem

We have a product of two binomials. Expanding this means multiplying each term in the first binomial by each term in the second binomial.

Using the FOIL Method

The FOIL method provides a systematic way to expand binomials:

  • First: Multiply the first terms of each binomial.
  • Outer: Multiply the outer terms of the binomials.
  • Inner: Multiply the inner terms of the binomials.
  • Last: Multiply the last terms of each binomial.

Let's apply FOIL to our expression:

  1. First: (1/5x) * (2/3x) = 2/15x²
  2. Outer: (1/5x) * (-y) = -1/5xy
  3. Inner: (2y) * (2/3x) = 4/3xy
  4. Last: (2y) * (-y) = -2y²

Combining Like Terms

Now we add the resulting terms:

2/15x² - 1/5xy + 4/3xy - 2y²

To simplify, we need to combine the xy terms:

2/15x² + (4/3 - 1/5)xy - 2y²

Find a common denominator for the xy terms (15):

2/15x² + (20/15 - 3/15)xy - 2y²

Combine the coefficients:

2/15x² + 17/15xy - 2y²

Conclusion

Therefore, the expanded form of (1/5x + 2y)(2/3x - y) is 2/15x² + 17/15xy - 2y².

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