(-3x^3+5x^2+10x+4)-(x^3+7x^2-3x+1)

Jasonbradley

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Jun 17, 2024

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Simplifying Polynomial Expressions

This article will guide you through the process of simplifying the following polynomial expression:

(-3x^3 + 5x^2 + 10x + 4) - (x^3 + 7x^2 - 3x + 1)

Understanding the Steps

To simplify this expression, we'll follow these steps:

1. Distribute the negative sign: The minus sign in front of the second set of parentheses means we multiply each term inside that set by -1.

2. Combine like terms: Identify terms with the same variable and exponent, and add their coefficients.

Simplifying the Expression

Let's apply these steps to our expression:

1. Distributing the negative sign:

   (-3x^3 + 5x^2 + 10x + 4) -1(x^3 + 7x^2 - 3x + 1)

   = -3x^3 + 5x^2 + 10x + 4 -x^3 - 7x^2 + 3x - 1

2. Combining like terms:

   -3x^3 - x^3 + 5x^2 - 7x^2 + 10x + 3x + 4 - 1

   = -4x^3 - 2x^2 + 13x + 3

Conclusion

Therefore, the simplified form of the expression (-3x^3 + 5x^2 + 10x + 4) - (x^3 + 7x^2 - 3x + 1) is -4x^3 - 2x^2 + 13x + 3.