Perform the indicated operations. (2x²-x)+(x²+4x)

Verified step by step guidance

1. Identify the expression to be simplified: \((2x^2 - x) + (x^2 + 4x)\).
2. Remove the parentheses since both are preceded by a plus sign, so the signs of the terms inside remain the same: \$2x^2 - x + x^2 + 4x$.
3. Group like terms together. Like terms are terms that have the same variable raised to the same power: \((2x^2 + x^2) + (-x + 4x)\).
4. Combine the coefficients of the like terms: \$2x^2 + x^2\( becomes \)(2 + 1)x^2\(, and \)-x + 4x\( becomes \)(-1 + 4)x$.
5. Write the simplified expression by combining the results: \((3x^2) + (3x)\).

Key Concepts

Polynomial Addition

Polynomial addition involves combining like terms from two or more polynomials. Like terms have the same variable raised to the same power. To add polynomials, align like terms and add their coefficients while keeping the variable part unchanged.

Like Terms

Like terms are terms in an expression that have identical variable parts with the same exponents. For example, 2x² and x² are like terms, but 2x² and 4x are not. Identifying like terms is essential for simplifying expressions correctly.

Combining Coefficients

When adding like terms, only the numerical coefficients are combined through addition or subtraction. For instance, adding 2x² and x² results in (2 + 1)x² = 3x². This process simplifies the polynomial into a more manageable form.