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 two polynomials. Like terms have the same variable raised to the same power. Here, the like terms are: \$5x^{2}\( and \)-4x^{2}\(, \)-4x\( and \)3x\(, and the constants \(7\) and \)-5$.
2. Set up the addition by grouping the like terms together: \((5x^{2} + (-4x^{2})) + (-4x + 3x) + (7 + (-5))\).
3. Perform the addition or subtraction for each group of like terms separately: add the coefficients of \(x^{2}\) terms, then the coefficients of \(x\) terms, and finally the constants.
4. Write the resulting polynomial by combining the simplified terms from each group, keeping the variable parts intact.
5. Check your final expression to ensure all like terms have been combined correctly and the polynomial is simplified.

Key Concepts

Polynomial Addition and Subtraction

Adding or subtracting polynomials involves combining like terms, which are terms with the same variable raised to the same power. You add or subtract their coefficients while keeping the variable part unchanged. This process simplifies the expression into a single polynomial.

Like Terms

Like terms are terms in a polynomial that have identical variable parts, including the same exponents. For example, 5x² and -4x² are like terms because both contain x squared. Recognizing like terms is essential for correctly performing addition or subtraction.

Distributive Property

The distributive property allows you to remove parentheses by distributing the addition or subtraction sign across each term inside the parentheses. For subtraction, this means changing the sign of each term in the second polynomial before combining like terms.