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

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

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

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

Expanding the Expression

First, we need to expand the expression by applying the distributive property and the rule for squaring a binomial:

  1. Expanding (2x+1)^2:

    • (2x+1)^2 = (2x+1)(2x+1)
    • = 4x^2 + 2x + 2x + 1
    • = 4x^2 + 4x + 1

  2. Expanding -2(2x^2-1):

    • -2(2x^2-1) = -4x^2 + 2

Combining Like Terms

Now that we have expanded the expression, we can combine like terms:

(4x^2 + 4x + 1) + (-4x^2 + 2) = 4x + 3

Final Result

Therefore, the simplified form of the expression (2x+1)^2 - 2(2x^2-1) is 4x + 3.

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