Peter Tran said:Homework Statement
Factor the following difference of two squares. Assume that variables represent whole numbers.
s^4 - 625
Homework Equations
(A)^2 - (B)^2
The Attempt at a Solution
s^4-625
(s^2)^2 - 25^2
(s^2+25)(s^2-25)
(s^2+25)(s+5)(s+5) - Correct
The "program" wants me to stop there, but why? Couldn't I just go ahead and continue factoring the (s^2+25) also?
Factoring is the process of breaking down an expression into smaller parts. However, not all expressions can be factored further. This could be due to a number of reasons, such as the expression being prime, having irrational numbers, or not following a specific pattern that allows for factoring.
Factoring an expression can help simplify it and make it easier to work with. It can also reveal important information about the expression, such as its roots, factors, or properties. In some cases, factoring can also help solve equations or problems more efficiently.
No, not every expression can be factored. Some expressions, such as prime numbers or irrational numbers, cannot be broken down into smaller parts. Additionally, some expressions may not follow a specific pattern that allows for factoring.
There are several methods for determining if an expression can be factored. One method is to look for common factors among the terms in the expression. If all the terms have a common factor, then the expression can be factored. Another method is to check if the expression follows a specific factoring pattern, such as the difference of squares or perfect square trinomial patterns.
There is no defined limit to how many times an expression can be factored. However, in most cases, factoring an expression multiple times will eventually lead to the same result. For example, factoring the expression (x+2)(x+3) will result in the same expression whether it is factored once or multiple times.