Add or subtract, as indicated. See Example 4. (5x² - 4x + 7) + (-4x² + 3x - 5)

Verified step by step guidance

1. Identify the like terms in the given polynomials: terms with the same variable raised to the same power.
2. Group the like terms together: $(5x^2-4x^2)+(-4x+3x)+(7-5)$.
3. Add or subtract the coefficients of the like terms: $5x^2-4x^2$, $-4x+3x$, and $7-5$.
4. Simplify each group of like terms to get the resulting polynomial.
5. Combine the simplified terms to write the final expression.

Key Concepts

Polynomial Addition

Polynomial addition involves combining like terms from two or more polynomials. Like terms are those that have the same variable raised to the same power. For example, in the expression (5x² - 4x + 7) + (-4x² + 3x - 5), you would add the coefficients of x², x, and the constant terms separately to simplify the expression.

Like Terms

Like terms are terms in a polynomial that share the same variable and exponent. Identifying like terms is crucial for simplifying polynomials, as they can be combined by adding or subtracting their coefficients. In the given expression, 5x² and -4x² are like terms, as are -4x and 3x, and the constants 7 and -5.

Combining Polynomials

Combining polynomials refers to the process of adding or subtracting polynomial expressions to form a single polynomial. This process requires careful attention to the signs of each term and the correct grouping of like terms. The result is a simplified polynomial that retains the same variable structure but has a new set of coefficients.