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(-a+1)(5a+6)

2 min read Jun 16, 2024
(-a+1)(5a+6)

Expanding the Expression (-a + 1)(5a + 6)

This article will guide you through expanding the expression (-a + 1)(5a + 6) using the FOIL method.

What is the FOIL method?

The FOIL method is a mnemonic acronym that stands for First, Outer, Inner, Last. It is used to multiply two binomials. Let's break it down:

  • 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.

Expanding the expression

  1. First: (-a) * (5a) = -5a²
  2. Outer: (-a) * (6) = -6a
  3. Inner: (1) * (5a) = 5a
  4. Last: (1) * (6) = 6

Now, add all the terms together:

-5a² - 6a + 5a + 6

Combine the like terms:

-5a² - a + 6

Conclusion

Therefore, the expanded form of (-a + 1)(5a + 6) is -5a² - a + 6. This method can be applied to any binomial multiplication problem.

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