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

MHB
Thread starter Abdullah Qureshi
Start date Mar 2, 2021
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Difference 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.

Mar 2, 2021

Abdullah Qureshi

Explain why x2 +1 is not a difference of squares and x2 -1 is

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Mar 2, 2021

skeeter

Oh, but it is ...

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

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.