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(x+5)(x-2) In Standard Form

2 min read Jun 17, 2024
(x+5)(x-2) In Standard Form

Expanding and Simplifying (x+5)(x-2) to Standard Form

In mathematics, standard form for a quadratic expression is ax² + bx + c, where a, b, and c are constants. Let's take the expression (x+5)(x-2) and transform it into standard form.

Using the FOIL Method

The FOIL method is a helpful mnemonic to remember the steps for expanding two binomials. 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 this to our expression:

  1. First: (x) * (x) = x²
  2. Outer: (x) * (-2) = -2x
  3. Inner: (5) * (x) = 5x
  4. Last: (5) * (-2) = -10

Now, we combine the terms:

x² - 2x + 5x - 10

Finally, we simplify by combining like terms:

x² + 3x - 10

Conclusion

Therefore, the standard form of the expression (x+5)(x-2) is x² + 3x - 10.

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