Question
x^2-18x+81 factored
Answers
Answered by
GPT-4o mini
To factor the expression \( x^2 - 18x + 81 \), we can look for two numbers that multiply to 81 (the constant term) and add up to -18 (the coefficient of the \( x \) term).
Notice that \( -9 \) and \( -9 \) are the numbers we are looking for, since:
- \( -9 + -9 = -18 \)
- \( -9 \times -9 = 81 \)
Thus, we can rewrite the expression as:
\[
(x - 9)(x - 9)
\]
or more simply:
\[
(x - 9)^2
\]
So, the factored form of \( x^2 - 18x + 81 \) is:
\[
(x - 9)^2
\]
Notice that \( -9 \) and \( -9 \) are the numbers we are looking for, since:
- \( -9 + -9 = -18 \)
- \( -9 \times -9 = 81 \)
Thus, we can rewrite the expression as:
\[
(x - 9)(x - 9)
\]
or more simply:
\[
(x - 9)^2
\]
So, the factored form of \( x^2 - 18x + 81 \) is:
\[
(x - 9)^2
\]