Perform the indicated operations. $(x^4-3x^2+2)-(-2x^4+x^2-3)$

Verified step by step guidance

1. Identify the expression to simplify: \((x^4 - 3x^2 + 2) - (-2x^4 + x^2 - 3)\).
2. Distribute the subtraction sign across the second polynomial, changing the signs of each term inside the parentheses: \((x^4 - 3x^2 + 2) + (2x^4 - x^2 + 3)\).
3. Group like terms together: \((x^4 + 2x^4) + (-3x^2 - x^2) + (2 + 3)\).
4. Combine the coefficients of like terms: add the coefficients of \(x^4\) terms, \(x^2\) terms, and constant terms separately.
5. Write the simplified expression by putting together the combined terms.

Key Concepts

Polynomial Expressions

Polynomial expressions are algebraic expressions consisting of variables raised to whole-number exponents and coefficients. Understanding how to identify terms, degrees, and coefficients is essential for performing operations like addition and subtraction on polynomials.

Subtraction of Polynomials

Subtracting polynomials involves changing the signs of the terms in the polynomial being subtracted and then combining like terms. Careful attention to distributing the negative sign across all terms is crucial to avoid errors.

Combining Like Terms

Combining like terms means adding or subtracting terms that have the same variable raised to the same power. This simplifies the expression and is a key step after performing addition or subtraction of polynomials.