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

2 min read Jun 16, 2024
(4x-1)(4x+1)-(x+3)^2

Expanding and Simplifying the Expression (4x-1)(4x+1)-(x+3)^2

This article will guide you through the process of expanding and simplifying the expression (4x-1)(4x+1)-(x+3)^2.

Expanding the Expression

Let's break down the expression step-by-step:

1. Expanding the first part:

  • The first part of the expression is (4x-1)(4x+1). This is a difference of squares pattern, which simplifies to: (4x)^2 - (1)^2 = 16x^2 - 1

2. Expanding the second part:

  • The second part is -(x+3)^2. This is a squared binomial pattern, which simplifies to: -(x^2 + 6x + 9) = -x^2 - 6x - 9

3. Combining the expanded parts:

  • Now we have: 16x^2 - 1 - x^2 - 6x - 9

Simplifying the Expression

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

  • 16x^2 - x^2 = 15x^2
  • -6x remains as it is
  • -1 - 9 = -10

Final Simplified Expression

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

15x^2 - 6x - 10

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