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(-m+5n)(-m-5n)

2 min read Jun 16, 2024
(-m+5n)(-m-5n)

Multiplying Binomials: (-m + 5n)(-m - 5n)

This article will guide you through multiplying the binomials (-m + 5n) and (-m - 5n). We'll use the FOIL method to make the process easier.

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.

Let's apply FOIL to our problem:

  1. First: (-m) * (-m) = m²
  2. Outer: (-m) * (-5n) = 5mn
  3. Inner: (5n) * (-m) = -5mn
  4. Last: (5n) * (-5n) = -25n²

Now, we add all the terms together:

m² + 5mn - 5mn - 25n²

Notice that the '5mn' and '-5mn' terms cancel each other out.

Therefore, the simplified product of (-m + 5n)(-m - 5n) is:

m² - 25n²

Key takeaway: This product is an example of a special product called the "difference of squares" pattern. The pattern arises when we multiply two binomials where one is the sum of two terms and the other is the difference of those same terms. The result is always the square of the first term minus the square of the second term.

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