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

2 min read Jun 16, 2024

Simplifying the Expression (2x-3)^2+(2x+3)^2-2(2x-3)(2x+3)

This expression might look intimidating at first, but it can be simplified using some basic algebraic identities and techniques. Let's break it down step-by-step:

Recognizing the Pattern

The expression resembles the expanded form of a difference of squares identity: (a-b)^2 + (a+b)^2 - 2(a-b)(a+b)

This pattern is very useful for simplifying expressions.

Applying the Identity

Let's substitute a = 2x and b = 3 in the given expression:

(2x-3)^2 + (2x+3)^2 - 2(2x-3)(2x+3) = (a-b)^2 + (a+b)^2 - 2(a-b)(a+b)

Now, using the difference of squares identity, we know: (a-b)^2 + (a+b)^2 - 2(a-b)(a+b) = 2a^2 + 2b^2

Substituting Back and Simplifying

Substitute a = 2x and b = 3 back into the equation:

2a^2 + 2b^2 = 2(2x)^2 + 2(3)^2 = 8x^2 + 18

Final Result

Therefore, the simplified form of the expression (2x-3)^2+(2x+3)^2-2(2x-3)(2x+3) is 8x^2 + 18.