- #1
Abdullah Qureshi
- 16
- 0
Explain why x2 +1 is not a difference of squares and x2 -1 is
The difference of squares is a term used to describe a polynomial that can be factored into two perfect squares with a subtraction sign between them. In the case of x^{2} +1 and x^{2} -1, neither of these expressions can be factored into two perfect squares. Therefore, they are not considered difference of squares.
Yes, both expressions can be factored, but not as difference of squares. x^{2} +1 can be factored into (x+1)(x+1), and x^{2} -1 can be factored into (x+1)(x-1).
The main difference between these two expressions is the sign between the x^{2} term and the constant term. In x^{2} +1, the sign is a plus (+), while in x^{2} -1, the sign is a minus (-).
Understanding the difference between these two expressions is important in algebra because it can help with factoring and solving equations. Knowing that x^{2} +1 and x^{2} -1 cannot be factored as difference of squares can save time and prevent errors when trying to factor them.
No, x^{2} +1 and x^{2} -1 can never be equal. This is because the constant term in x^{2} +1 is 1, while the constant term in x^{2} -1 is -1. Therefore, they will always have a difference of 2, making them unequal.