(2x+3)^2-2(2x+3)(2x+5)+(2x+5)^2

2 min read Jun 16, 2024

Simplifying the Expression (2x+3)^2 - 2(2x+3)(2x+5) + (2x+5)^2

This expression looks complicated, but we can simplify it using a few key algebraic techniques. Let's break it down step by step.

Recognizing the Pattern

Notice that the expression resembles the expansion of a squared binomial: (a - b)^2 = a^2 - 2ab + b^2.

In our case:

a = (2x+3)
b = (2x+5)

Applying the Pattern

Substituting these values into the pattern, we get:

[(2x+3) - (2x+5)]^2

Simplifying the Expression

Simplify the terms inside the brackets: (2x + 3) - (2x + 5) = -2
Square the simplified term: (-2)^2 = 4

Therefore, the simplified expression is 4.

Conclusion

The expression (2x+3)^2 - 2(2x+3)(2x+5) + (2x+5)^2 simplifies to the constant 4. This simplification is possible by recognizing the pattern of a squared binomial and applying it to the given expression.