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(x+2)+(x-2)(2x+1)

less than a minute read Jun 16, 2024
(x+2)+(x-2)(2x+1)

Simplifying the Expression (x + 2) + (x - 2)(2x + 1)

This article will guide you through the process of simplifying the algebraic expression (x + 2) + (x - 2)(2x + 1).

Step 1: Expanding the Product

The first step is to expand the product of the two binomials (x - 2)(2x + 1) using the distributive property (also known as FOIL method).

  • First: x * 2x = 2x²
  • Outer: x * 1 = x
  • Inner: -2 * 2x = -4x
  • Last: -2 * 1 = -2

Therefore, (x - 2)(2x + 1) = 2x² - 3x - 2

Step 2: Combining Like Terms

Now, substitute the expanded expression back into the original equation:

(x + 2) + (2x² - 3x - 2)

Combine the like terms:

  • x + 2x² - 3x - 2 + 2

This simplifies to: 2x² - 2x

Conclusion

The simplified form of the expression (x + 2) + (x - 2)(2x + 1) is 2x² - 2x.

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