Final answer:
A) 5r² - 4r - 4 Then, combine the coefficients of the linear terms (-9r and -5r), giving -4r. Lastly, add the constants (1 and -3), resulting in -4. Thus, the simplified expression is 5r² - 4r - 4, which matches option A.
Explanation:
The expression (4r² – 9r + 1) + (r² – 5r – 3) simplifies to 5r² - 4r - 4. To simplify this expression, combine like terms by adding or subtracting coefficients of similar monomials. Start by combining the terms with the same variables raised to the same power. In this case, add the coefficients of the quadratic terms (4r² and r²), which results in 5r².
Then, combine the coefficients of the linear terms (-9r and -5r), giving -4r. Lastly, add the constants (1 and -3), resulting in -4. Thus, the simplified expression is 5r² - 4r - 4, which matches option A.
This simplification process involves gathering terms with similar powers of the variable (in this case, 'r') and performing arithmetic operations (addition and subtraction) with their coefficients. By systematically combining like terms, the expression condenses into a more manageable and simplified form, adhering to the principles of algebraic simplification.