(4x^5-3x^3+2x^2-7)-(x^4+2x^3-4x-3)

Jasonbradley

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Jun 16, 2024

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Simplifying Polynomial Expressions

This article will guide you through simplifying the polynomial expression: (4x^5 - 3x^3 + 2x^2 - 7) - (x^4 + 2x^3 - 4x - 3).

Understanding the Steps

1. Distribute the negative sign: Remember that subtracting a polynomial is the same as adding its negative. This means we distribute the negative sign to every term inside the second set of parentheses.

2. Combine like terms: Once the negative sign is distributed, we combine terms with the same variable and exponent.

Applying the Steps

Let's break down the process step by step:

1. Distribute the negative sign:

   (4x^5 - 3x^3 + 2x^2 - 7) - (x^4 + 2x^3 - 4x - 3) 
   = 4x^5 - 3x^3 + 2x^2 - 7 - x^4 - 2x^3 + 4x + 3
   

2. Combine like terms:

   = 4x^5 - x^4 - 3x^3 - 2x^3 + 2x^2 + 4x - 7 + 3 
   = **4x^5 - x^4 - 5x^3 + 2x^2 + 4x - 4**
   

Conclusion

By applying the principles of distributing negative signs and combining like terms, we have successfully simplified the polynomial expression to 4x^5 - x^4 - 5x^3 + 2x^2 + 4x - 4.