In 1–2 sentences, explain why the following operation is a closed system under subtraction.
(9x^2 + 17x + 13) − (2x^2 + 12x + 11)
The operation of subtraction is a closed system because it yields a polynomial with real coefficients when subtracting two polynomials with real coefficients.
Use the Distributive Property to prove that these algebraic expressions are equivalent. Explain your answer in one sentence for each expression and show your work.
Expression 1: (x − 5) * (x + 3)
Expression 2: 2x^2 − x2 − 2x − 20 + 5