%5E2-answer.jpeg "(2x-5y)^2 Answer")
Expanding the Square of a Binomial: (2x - 5y)^2
The expression (2x - 5y)^2 represents the square of a binomial, which is a polynomial with two terms. To expand this expression, we can utilize the concept of FOIL (First, Outer, Inner, Last) or the square of a difference formula.
Expanding using FOIL
FOIL stands for:
- 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.
Applying FOIL to (2x - 5y)^2:
- First: (2x) * (2x) = 4x^2
- Outer: (2x) * (-5y) = -10xy
- Inner: (-5y) * (2x) = -10xy
- Last: (-5y) * (-5y) = 25y^2
Adding the results:
4x^2 - 10xy - 10xy + 25y^2 = 4x^2 - 20xy + 25y^2
Using the Square of a Difference Formula
The square of a difference formula states: (a - b)^2 = a^2 - 2ab + b^2
In this case, a = 2x and b = 5y. Applying the formula:
(2x - 5y)^2 = (2x)^2 - 2(2x)(5y) + (5y)^2
Simplifying:
(2x - 5y)^2 = 4x^2 - 20xy + 25y^2
Conclusion
Both methods yield the same answer: 4x^2 - 20xy + 25y^2. Expanding (2x - 5y)^2 results in a trinomial, where the first and last terms are squares of the original binomial terms, and the middle term is twice the product of the original terms. Remember, when squaring a binomial, it's crucial to remember the sign of the middle term, which is negative in this case.