Find the product of the expression (x-9)^2.
Understand the Problem
The question requires us to find the product of the expression (x-9)^2. This means we need to expand the expression (x-9)(x-9) using the distributive property (also known as the FOIL method) and simplify.
Answer
$x^2 - 18x + 81$
Answer for screen readers
$x^2 - 18x + 81$
Steps to Solve
- Write out the expression
We need to expand $(x-9)^2$. This is the same as $(x-9)(x-9)$.
- Apply the distributive property (FOIL method)
We multiply each term in the first parentheses with each term in the second parentheses:
$x * x + x * (-9) + (-9) * x + (-9) * (-9)$
-
Simplify the multiplication $x^2 - 9x - 9x + 81$
-
Combine like terms
Combine the $x$ terms:
$x^2 - 18x + 81$
$x^2 - 18x + 81$
More Information
The expansion of $(x-9)^2$ results in a quadratic expression. This type of problem is common in algebra and is used in many applications, such as finding the roots of a quadratic equation or graphing quadratic functions.
Tips
A common mistake is to simply square each term inside the parentheses, which would give $x^2 + 81$. This is incorrect because it neglects the middle term that results from the distributive property (FOIL method). Remember to multiply $(x-9)(x-9)$ completely.
AI-generated content may contain errors. Please verify critical information
