factor x^2 - 100?

Answer 1

x^2 - 100 =
x^2 - 10^2 =
(x-10)(x+10)
Th

Answer 2

The general formula for factoring a polynomial in the form (a^2-b^2) is (a+b)(a-b). Thus:

x^2 - 100 = (x + 10)(x - 10)

Answer 3

(a**2 - b**2) = (a+b)(a-b)

so x**2 - 100 = x**2 - 10*2 = (x+10)(x-10)

Answer 4

x² - 100

(x - 10) (x + 10) = x² - 10x + 10x - 100

The - 10x and + 10x cancel

The factor is (x - 10) (x + 10)

The answer is (x - 10)(x + 10)

Answer 5

x²-100=x²-10²=(x-10)*(x+10)

The formula is
x²-a²=(x-a)*(x+a)

--Your Checking your answer--
You can do a check to see that this is correct.
Expand this function: f(x)=(x-a)*(x+a)
I'm doing all of the steps to help you in learning your Math
So
(x-a)*(x+a)=x*(x+a)-a*(x+a)=
x²+ax-ax-a²=x²-a²
--end of checking answer---

So, now you can factor this for any equation of this form of x²-a².

Here's More Practice for you to do to study for your test. By the way alt key + 253 on keypad gives you ², in other words the power of two.
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Try these:
Factor:
1) x²-16
2) x²-256
3) x²-10^4
5) x^4-10^4
I'll answer #5 for you. You finish it.
x^4-10^4=(x²-10²)*(x²+10²)
Now you finish factoring this. It's easy now!
6) x^8-2^8
7) y²-x²
8) (x+1)²-(x-1)²
I'll do #8 for you.
(x+1)²-(x-1)²=
((x+1)+(x-1))*((x+1)-(x-1))
=(2x)*(x+1-x+1)=(2x)*(2)
=4x
9) (x+2)²-x²
10) (x²-2x+1)²-(x²+2x-1)²
I'll do #10 for you
(x²-2x+1)²-(x²+2x-1)²=
[(x²-2x+1)-(x²+2x-1)]*
[(x²-2x+1)+(x²+2x-1)]=
[-4x+2]*[2x²]=
2*(-2x+1)*2*x²=
4*x²*(1-2*x)=4x²(1-2x)
11) x²-4
12) x²-2
13) x²-100²
14) x²+2
answer, nope you can't factor this in the Real Number System.
#12 I assume that you know that the square root of numbers, such as sqr of 2 is called
sqr(2).
Last One to study for your test:
15) x²-(x-1)²
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I hope that this practice help you study for your test. I was a Math Major who had a Teaching Assistantship in an Applied Mathematics Masters Program (MS in Applied Math, MS in Pure Math with over 100 grad credits in Math toward a Phd in Math, BS in Math). I love to teach at the University Level as well as to tutor Math.

Answer 6

(x-10)(x+10)

solution:
x^2+10x-10x-100
cancel +10x and -10x which is zero

it equals to x^2-100

Answer 7

(x-10)(x+10)

Answer 8

(x-10)(x+10)

Answer 9

Use difference of squares formula.

Try this link for help:
http://www.purplemath.com/modules/specfact.htm