%5E2-6(x%5E2%2B1)%2B9.jpeg "(x^2+1)^2-6(x^2+1)+9")
Factoring the Expression (x^2 + 1)^2 - 6(x^2 + 1) + 9
This expression can be factored using the pattern of a perfect square trinomial. Let's break it down step by step:
1. Recognizing the Pattern:
The expression resembles the form of a perfect square trinomial: (a - b)^2 = a^2 - 2ab + b^2
2. Identifying a and b:
In our expression, (x^2 + 1) plays the role of 'a' and 3 plays the role of 'b'. Notice that:
- (x^2 + 1)^2 corresponds to a^2
- -6(x^2 + 1) corresponds to -2ab (since -6 = -2 * 3)
- 9 corresponds to b^2 (since 9 = 3^2)
3. Factoring the Expression:
Following the pattern, we can factor the expression as:
(x^2 + 1)^2 - 6(x^2 + 1) + 9 = (x^2 + 1 - 3)^2
4. Simplifying the Result:
Simplifying the expression further, we get:
(x^2 + 1 - 3)^2 = (x^2 - 2)^2
Therefore, the factored form of the expression (x^2 + 1)^2 - 6(x^2 + 1) + 9 is (x^2 - 2)^2.