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(x+5)(x-4)

2 min read Jun 17, 2024
(x+5)(x-4)

Expanding (x+5)(x-4)

The expression (x+5)(x-4) is a product of two binomials. To expand this expression, we can use the FOIL method (First, Outer, Inner, Last).

FOIL Method

  1. First: Multiply the first terms of each binomial:

    • x * x = x²

  2. Outer: Multiply the outer terms of each binomial:

    • x * -4 = -4x

  3. Inner: Multiply the inner terms of each binomial:

    • 5 * x = 5x

  4. Last: Multiply the last terms of each binomial:

    • 5 * -4 = -20

Combining Terms

Now, we combine all the terms:

  • x² - 4x + 5x - 20

Finally, we simplify the expression by combining the like terms:

  • x² + x - 20

Therefore, the expanded form of (x+5)(x-4) is x² + x - 20.

Alternative Methods

You can also expand the expression using the distributive property:

  • (x+5)(x-4) = x(x-4) + 5(x-4)
  • = x² - 4x + 5x - 20
  • = x² + x - 20

No matter which method you choose, the result is the same.

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