Question

multiply using foil. write the answer in standard form.
1
$(x + 5)(x + 8)$
2
$(x + 1)(x - 1)$
3
$(x + 3)(x - 5)$

Explanation:

Problem 1: \((x + 5)(x + 8)\)

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

First: \(x \cdot x = x^2\)
Outer: \(x \cdot 8 = 8x\)
Inner: \(5 \cdot x = 5x\)
Last: \(5 \cdot 8 = 40\)

Step 2: Combine like terms

\(x^2 + 8x + 5x + 40 = x^2 + 13x + 40\)

Step 1: Apply FOIL

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

Step 2: Combine like terms

\(x^2 - x + x - 1 = x^2 - 1\) (the \(-x\) and \(x\) cancel out)

Step 1: Apply FOIL

First: \(x \cdot x = x^2\)
Outer: \(x \cdot (-5) = -5x\)
Inner: \(3 \cdot x = 3x\)
Last: \(3 \cdot (-5) = -15\)

Step 2: Combine like terms

\(x^2 - 5x + 3x - 15 = x^2 - 2x - 15\)

Answer:

\(x^2 + 13x + 40\)

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