(2%2F3x%2B4%2F5y).jpeg "(2/3x+4/5y)(2/3x+4/5y)")
Expanding the Expression (2/3x + 4/5y)(2/3x + 4/5y)
This expression represents the product of two identical binomials. We can expand it using the FOIL method (First, Outer, Inner, Last), or by applying the square of a binomial formula.
Using the FOIL Method
First: (2/3x) * (2/3x) = 4/9x² Outer: (2/3x) * (4/5y) = 8/15xy Inner: (4/5y) * (2/3x) = 8/15xy Last: (4/5y) * (4/5y) = 16/25y²
Now, combine the like terms:
4/9x² + 8/15xy + 8/15xy + 16/25y² = 4/9x² + 16/15xy + 16/25y²
Using the Square of a Binomial Formula
The square of a binomial formula states: (a + b)² = a² + 2ab + b²
Applying this to our expression:
(2/3x + 4/5y)² = (2/3x)² + 2 * (2/3x) * (4/5y) + (4/5y)²
Expanding:
= 4/9x² + 16/15xy + 16/25y²
Conclusion
Both methods lead to the same result: (2/3x + 4/5y)(2/3x + 4/5y) = 4/9x² + 16/15xy + 16/25y²
This expanded form is useful for various purposes, such as solving equations, factoring expressions, or understanding the relationship between the original binomial and its squared form.