Hello! I am studying for an upcoming math test and I'm trying to figure out how to solve this equation:
Select the expression that is equivalent to (m^2 - 25).
A. (m^2 - 10m + 25)
B. (m^2 + 10m + 25)
C. (m - 5) (m + 5)
D. (m - 5)^2
I do NOT want the answer to this. I just want to know how to solve it, because in the test there will be something similar to it. So if there's any tricks or tips that you have to solve this, please do share!
Try simplifying each of the choices into a variable and a number.
Oh wow! That trick actually worked so easily! Thank you! From this, I got the answer was C, then?
yes
and review: the difference between two squares!
To determine which expression is equivalent to (m^2 - 25), we need to understand the difference of squares formula. The formula states that if we have an expression in the form (a^2 - b^2), it can be factored as (a + b)(a - b).
In our equation, (m^2 - 25), we can rewrite 25 as 5^2. So the equation becomes (m^2 - 5^2), which is in the form (a^2 - b^2), with a = m and b = 5.
Now we can apply the difference of squares formula and factor the equation as follows:
(m^2 - 5^2) = (m + 5)(m - 5)
So, the expression (m^2 - 25) is equivalent to (m + 5)(m - 5). In the given options, the corresponding expression is (C) (m - 5)(m + 5).
Remember to look for patterns and familiar formulas, like the difference of squares, when solving algebraic equations. These can often simplify the process and help you to arrive at the correct answer.