Question

multiply using foil then answer the questions.

1. $(x + 8)(x - 1)$ 3. $(x + 4)(x - 2)$
2. $(x - 8)(x + 1)$ 4. $(x - 4)(x + 2)$
3. is each product a binomial, trinomial or polynomial?
4. for problems 1 & 2 and 3 & 4, what do you notice that is different between the problems?
5. for problems 1 & 2 and 3 & 4, what do you notice that is different about the answers?

Explanation:

Problem 1: \((x + 8)(x - 1)\)

Step 1: Apply FOIL (First, Outer, Inner, Last)

First: \(x \cdot x = x^2\)
Outer: \(x \cdot (-1) = -x\)
Inner: \(8 \cdot x = 8x\)
Last: \(8 \cdot (-1) = -8\)

Step 2: Combine like terms

\(x^2 - x + 8x - 8 = x^2 + 7x - 8\)

Step 1: Apply FOIL

First: \(x \cdot x = x^2\)
Outer: \(x \cdot 1 = x\)
Inner: \(-8 \cdot x = -8x\)
Last: \(-8 \cdot 1 = -8\)

Step 2: Combine like terms

\(x^2 + x - 8x - 8 = x^2 - 7x - 8\)

Step 1: Apply FOIL

First: \(x \cdot x = x^2\)
Outer: \(x \cdot (-2) = -2x\)
Inner: \(4 \cdot x = 4x\)
Last: \(4 \cdot (-2) = -8\)

Step 2: Combine like terms

\(x^2 - 2x + 4x - 8 = x^2 + 2x - 8\)

Answer:

\(x^2 + 7x - 8\)

Problem 2: \((x - 8)(x + 1)\)