(-x+2)^2-5(-x+2)-15

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression (-x+2)^2-5(-x+2)-15

This article will guide you through simplifying the algebraic expression (-x+2)^2-5(-x+2)-15.

Understanding the Expression

The expression involves a combination of:

• Squaring a binomial: (-x+2)^2
• Multiplying a binomial by a constant: -5(-x+2)
• Adding and subtracting constants: -15

Simplifying Step-by-Step

1. Expand the square:

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

2. Distribute the constant:

   • -5(-x+2) = 5x - 10

3. Combine all terms:

   • x^2 - 4x + 4 + 5x - 10 - 15

4. Simplify by combining like terms:

   • x^2 + x - 21

Final Result

The simplified form of the expression (-x+2)^2-5(-x+2)-15 is x^2 + x - 21.

Additional Notes

• Factoring: The simplified expression (x^2 + x - 21) can be factored, but it doesn't result in a simple factorization.
• Solving for x: If you were asked to solve for x, you would need to set the expression equal to zero and then use methods like the quadratic formula or factoring to find the solutions.

This article provides a basic walkthrough of simplifying the given expression. Remember, understanding the order of operations and how to expand and distribute terms is essential for simplifying algebraic expressions.