(2a^2b-5b^3+4a^4b^2)-(7b^3+8a^4b^2-7a^2b)

Jasonbradley

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Jun 16, 2024

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Simplifying Polynomial Expressions

This article will guide you through the process of simplifying the polynomial expression: (2a^2b-5b^3+4a^4b^2)-(7b^3+8a^4b^2-7a^2b)

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 the parentheses by -1.
2. Combine like terms: We group terms with the same variable and exponent together.
3. Simplify: Add or subtract the coefficients of the like terms.

Simplifying the Expression

Let's apply the steps to our expression:

1. Distribute the negative sign: (2a^2b - 5b^3 + 4a^4b^2) + (-7b^3 - 8a^4b^2 + 7a^2b)

2. Combine like terms: (2a^2b + 7a^2b) + (-5b^3 - 7b^3) + (4a^4b^2 - 8a^4b^2)

3. Simplify: 9a^2b - 12b^3 - 4a^4b^2

Conclusion

Therefore, the simplified form of the polynomial expression (2a^2b-5b^3+4a^4b^2)-(7b^3+8a^4b^2-7a^2b) is 9a^2b - 12b^3 - 4a^4b^2. Remember to always pay attention to the signs when distributing and combining like terms.