(2%2F3x-y).jpeg "(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:
- First: (1/5x) * (2/3x) = 2/15x²
- Outer: (1/5x) * (-y) = -1/5xy
- Inner: (2y) * (2/3x) = 4/3xy
- 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.