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

Jasonbradley

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Jun 17, 2024

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

This article will guide you through simplifying the given expression: (x-2)^2 + (x+1)^2 + 2(x-2)(-1-x). We'll use the concepts of algebraic expansion and factorization to arrive at the simplest form.

Expanding the Expression

First, let's expand each of the terms in the expression using the following formulas:

• (a - b)^2 = a^2 - 2ab + b^2
• (a + b)^2 = a^2 + 2ab + b^2

Applying these formulas, we get:

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

Now, our expression becomes:

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

Combining Like Terms

Next, we combine the terms with the same variable and exponent:

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

This simplifies to:

0 + 0 + 9

Final Result

Therefore, the simplified form of the expression (x-2)^2 + (x+1)^2 + 2(x-2)(-1-x) is 9.

This result demonstrates that the given expression is a constant value, independent of the variable 'x'.