Question

In 1–2 sentences, explain why the following operation is a closed system under subtraction.

(9x^2 + 17x + 13) − (2x^2 + 12x + 11)

Answer 1

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

Answer 2

The operation of subtraction is a closed system because it yields a polynomial with real coefficients when subtracting two polynomials with real coefficients.

Answer 3

Expression 1: (x - 5) * (x + 3) is equivalent to Expression 2: 2x^2 - x^2 - 2x - 20 + 5, because when using the Distributive Property, the first term in Expression 1 distributes to the terms in Expression 2: x * (x + 3) and -5 * (x + 3), resulting in the same terms.