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(x-5y)^2

2 min read Jun 17, 2024
(x-5y)^2

Expanding (x - 5y)^2

In mathematics, squaring a binomial like (x - 5y)^2 often requires understanding the concept of FOIL (First, Outer, Inner, Last). This method helps us systematically multiply the terms within the binomial.

Here's how to expand (x - 5y)^2 using FOIL:

  1. First: Multiply the first terms of each binomial: x * x = x²
  2. Outer: Multiply the outer terms of the binomials: x * (-5y) = -5xy
  3. Inner: Multiply the inner terms of the binomials: (-5y) * x = -5xy
  4. Last: Multiply the last terms of each binomial: (-5y) * (-5y) = 25y²

Now, we combine all the terms: x² - 5xy - 5xy + 25y²

Finally, simplify by combining the like terms: x² - 10xy + 25y²

Therefore, the expanded form of (x - 5y)² is x² - 10xy + 25y².

Key Points:

  • Remember FOIL: This method helps ensure you multiply every term in the binomials.
  • Simplify: Always combine like terms for a simplified answer.
  • Practice: Expanding binomials becomes easier with practice.

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