(x-y)(x-y) Answer

2 min read Jun 17, 2024
(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.

  1. First: Multiply the first terms of each binomial: x * x = x²
  2. Outer: Multiply the outer terms of the binomials: x * -y = -xy
  3. Inner: Multiply the inner terms of the binomials: -y * x = -xy
  4. 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.

  1. Distribute the first term: x(x-y) = x² - xy
  2. 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.

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