Why x2 +1 and x2 -1 are Not/Are Difference of Squares

In summary, the difference of squares is an algebraic expression or polynomial that can be factored into two perfect square terms. It is represented by the form of a^2 - b^2, where a and b are real numbers. X^2 + 1 and x^2 - 1 are not difference of squares, as they do not have two perfect square terms as factors. Understanding the difference of squares is important in algebra because it aids in factoring and solving equations more efficiently, and helps identify patterns and relationships between different expressions.
  • #1
Abdullah Qureshi
16
0
Explain why x2 +1 is not a difference of squares and x2 -1 is
 
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  • #2
Oh, but it is ...

$x^2+1 = x^2 - (-1) = (x - i)(x + i)$
 

FAQ: Why x2 +1 and x2 -1 are Not/Are Difference of Squares

1. Why are x2 +1 and x2 -1 not considered difference of squares?

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 x2 +1 and x2 -1, neither of these expressions can be factored into two perfect squares. Therefore, they are not considered difference of squares.

2. Can x2 +1 and x2 -1 be factored at all?

Yes, both expressions can be factored, but not as difference of squares. x2 +1 can be factored into (x+1)(x+1), and x2 -1 can be factored into (x+1)(x-1).

3. What is the difference between x2 +1 and x2 -1?

The main difference between these two expressions is the sign between the x2 term and the constant term. In x2 +1, the sign is a plus (+), while in x2 -1, the sign is a minus (-).

4. Why is it important to understand the difference between x2 +1 and x2 -1?

Understanding the difference between these two expressions is important in algebra because it can help with factoring and solving equations. Knowing that x2 +1 and x2 -1 cannot be factored as difference of squares can save time and prevent errors when trying to factor them.

5. Can x2 +1 and x2 -1 ever be equal?

No, x2 +1 and x2 -1 can never be equal. This is because the constant term in x2 +1 is 1, while the constant term in x2 -1 is -1. Therefore, they will always have a difference of 2, making them unequal.

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