(x-y)-answer.jpeg "(x-y)(x-y) Answer")
Understanding (x-y)(x-y)
The expression (x-y)(x-y) is a common algebraic expression that can be simplified using the FOIL method or the distributive property.
Using the FOIL Method
FOIL stands for First, Outer, Inner, Last, and it's a systematic way to multiply two binomials.
- First: Multiply the first terms of each binomial: x * x = x²
- Outer: Multiply the outer terms of the binomials: x * -y = -xy
- Inner: Multiply the inner terms of the binomials: -y * x = -xy
- Last: Multiply the last terms of each binomial: -y * -y = y²
Now, combine the terms: x² - xy - xy + y²
Finally, simplify by combining like terms: x² - 2xy + y²
Using the Distributive Property
The distributive property states that a(b+c) = ab + ac.
- Distribute the first term: x(x-y) = x² - xy
- Distribute the second term: -y(x-y) = -xy + y²
Now, combine the terms: x² - xy - xy + y²
Finally, simplify by combining like terms: x² - 2xy + y²
Conclusion
Both methods lead to the same simplified answer: x² - 2xy + y². This expression is a perfect square trinomial, which is a special case of a trinomial that results from squaring a binomial.
Understanding how to multiply binomials is essential for various algebraic operations, including solving equations, factoring expressions, and simplifying expressions.