What is the difference between x squared -25 and
x squared -25x ? It's part of a problem I can't figure and I can't seem to find similar problems in my book. Would anyone care to explain it to me?
Sorry, I can't even figure out how to type x squared without having to type it all out.
2006-12-30 12:17:54 · 5 answers · asked by Kaari P 2 in Education & Reference ➔ Homework Help
x^2 - 25 has no middle term; there is no plain old "x" in the problem. When you factor this problem, it turns into (x + 5)(x - 5). If you multiply the two together, you get:
x^2 + 5x - 5x -25
The "x" term drops out, so you get x^2 - 25.
x^2 - 25x, on the other hand, would factor out to be (x - 25)(x + 0), I believe. The only difference between the two that I see is that the first one (x^2 - 25) is one of a special kind of problem that will always factor in the same way--there's a special name for them, but I don't remember it. Any problem that follows the format of
x^2 - perfect square will always factor out into
(x + square root)(x - square root).
Example: x^2 - 36 factors to (x + 6)(x - 6)
I'm sorry I can't remember the name of the problems, but I hope you get the general concept as to why the two are different.
2006-12-30 12:30:50 · answer #1 · answered by AskerOfQuestions 3 · 1⤊ 0⤋
I agree...re-write each problem in its factored form and you'll see the difference:
x squared - 25 = (x-5)(x+5)
x squared - 25x = x (x-25)
2006-12-30 20:25:45 · answer #2 · answered by katelle 2 · 1⤊ 0⤋
because you're multiplying an extra x onto the problem. Take the -25x and remove the extra x.
2006-12-30 20:20:51 · answer #3 · answered by kaizoku 3 · 0⤊ 1⤋
X2-25 is (X+5)x(X-5). X2-25X is X(X-25)
2006-12-30 20:24:58 · answer #4 · answered by fuzhou43 2 · 1⤊ 0⤋
you have 2 x's instead of 1
2006-12-30 22:06:45 · answer #5 · answered by Anonymous · 0⤊ 1⤋