(-2x^4-4y^3+4z^3+6)-(-9x^4-3y^3+4z^3+9)

Jasonbradley

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Jun 16, 2024

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Simplifying Polynomial Expressions

In mathematics, simplifying polynomial expressions involves combining like terms and reducing the expression to its simplest form. Let's take a look at an example:

Problem:

Simplify the following polynomial expression:

(-2x^4 - 4y^3 + 4z^3 + 6) - (-9x^4 - 3y^3 + 4z^3 + 9)

Solution:

1. Distribute the negative sign:

   The minus sign in front of the second set of parentheses indicates that we need to multiply each term inside the parentheses by -1.

   (-2x^4 - 4y^3 + 4z^3 + 6) + 9x^4 + 3y^3 - 4z^3 - 9

2. Combine like terms:

   Identify terms with the same variables and exponents.

   ( -2x^4 + 9x^4 ) + ( -4y^3 + 3y^3 ) + ( 4z^3 - 4z^3 ) + ( 6 - 9 )

3. Simplify:

   Combine the coefficients of like terms.

   7x^4 - y^3 + 0 - 3

Final Answer:

The simplified form of the expression is 7x^4 - y^3 - 3.