2-answer.jpeg "(x-5y)2 Answer")
Expanding (x - 5y)2
The expression (x - 5y)2 represents the square of a binomial, which is a polynomial with two terms. To expand this, we can apply the FOIL method (First, Outer, Inner, Last) or the Square of a Binomial formula.
Using the FOIL Method
- First: Multiply the first terms of each binomial: x * x = x²
- Outer: Multiply the outer terms: x * (-5y) = -5xy
- Inner: Multiply the inner terms: (-5y) * x = -5xy
- Last: Multiply the last terms: (-5y) * (-5y) = 25y²
Now, add all the terms together: x² - 5xy - 5xy + 25y² = x² - 10xy + 25y²
Using the Square of a Binomial Formula
The formula for squaring a binomial is: (a - b)² = a² - 2ab + b²
In this case, a = x and b = 5y. Substituting these values into the formula:
x² - 2(x)(5y) + (5y)² = x² - 10xy + 25y²
Conclusion
Both methods lead to the same result: (x - 5y)² = x² - 10xy + 25y². It's important to remember that squaring a binomial results in a trinomial (a polynomial with three terms) where the middle term is twice the product of the terms in the binomial.