Question

Simplify the expression.
Then, in 1 sentences, explain how multiplying polynomials is a closed system. In a 4th graders response
(X^2- 1) (-2x + 5)

Answer 1

To simplify the expression \((X^2 - 1)(-2x + 5)\), we can use the distributive property (often called the FOIL method for binomials):

1. First, distribute \(-2x\) to both terms in \((X^2 - 1)\):
\(-2x \cdot X^2 = -2X^3\)
\(-2x \cdot (-1) = 2x\)

2. Next, distribute \(5\) to both terms in \((X^2 - 1)\):
\(5 \cdot X^2 = 5X^2\)
\(5 \cdot (-1) = -5\)

Now, combine all the terms:
\[-2X^3 + 5X^2 + 2x - 5.\]

So, the simplified expression is:
\(-2X^3 + 5X^2 + 2x - 5\).

Multiplying polynomials is a closed system because when you multiply two polynomial expressions, you always get another polynomial as the result.