Convert (x+1)(x-1) to Its Standard Quadratic Form

To solve this problem and find the standard representation of the function $f(x) = (x+1)(x-1)$, we will expand the product using the distributive property, often recalled as FOIL (First, Outer, Inner, Last) for the product of two binomials.

Let's proceed step-by-step:

• Step 1: Apply the distributive property:
  $f(x) = (x+1)(x-1)$ would become:
• First terms: $x \cdot x = x^2$
• Outer terms: $x \cdot (-1) = -x$
• Inner terms: $1 \cdot x = x$
• Last terms: $1 \cdot (-1) = -1$

Step 2: Combine all the terms obtained from the FOIL method:
$x^2 - x + x - 1$

Step 3: Simplify the expression by combining like terms:
The terms $-x$ and $x$ cancel each other out, simplifying to:
$f(x) = x^2 - 1$

Thus, the standard representation of the function is $f(x) = x^2 - 1$.