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

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression: (2x+1)^2 + 2(4x^2-1) + (2x-1)^2

This expression involves squaring binomials and simplifying terms. Let's break down the process step-by-step:

Expanding the Binomials

First, we'll expand the squared binomials using the formula (a + b)^2 = a^2 + 2ab + b^2 and (a - b)^2 = a^2 - 2ab + b^2:

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

Substituting and Simplifying

Now, let's substitute the expanded forms back into the original expression:

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

Next, we distribute the 2:

(4x^2 + 4x + 1) + 8x^2 - 2 + (4x^2 - 4x + 1)

Finally, combine like terms:

(4x^2 + 8x^2 + 4x^2) + (4x - 4x) + (1 - 2 + 1)

The Simplified Expression

After simplifying, we are left with:

16x^2

Therefore, the simplified form of the expression (2x+1)^2 + 2(4x^2-1) + (2x-1)^2 is 16x^2.