math problem again?

Question

http://regentsprep.org/Regents/math/factor/PracFact1.htm
well, please visit this site and tell me what does the last task mean, I just don't understand the smaller 2, what is it? please give me a clearer picture.

Answer 1

(x - 1)² - 4

First FOIL (x - 1)²

(x - 1)(x - 1) = x² - x - x + 1 = x² - 2x + 1

x² - 2x + 1 - 4 =

x² - 2x - 3

The factor of x² - 2x - 3 =

(x - 3)(x + 1)

- - - - - -s-

Answer 2

it means the same thing as all of the other "small 2"s.

you understand x^2, right? let's say x = 4. then x^2 = 16.
what might be confusing is that you are squaring the entire expression in the parentheses. but again, let's say that x=4.
but now we want (x-1)^2. this is easy too, right? x-1 = 3, and 3^2 = 9. therefore (x-1)^2 = 9.

I would not be surprised if you have not been taught how to expand this kind of expression yet.
(x-1)^2
expands into
x^2 -2x +1
(square the first term, two times the product of 1st term and 2nd term, then square of the 2nd term)

subtract 4 as the problem says, and you have
x^2 - 2x - 3

now factor this to receive
(x-3)(x+1)
which is your answer.

Answer 3

9y^2-49
Q. What times what will render 9?
A. Three
Q.What times what will render forty-nine?
A. Seven
so we get (3y-7)(3y+7)

(x-1)^2-4 Not sure, but I'll take a stab.

(X+1)-2 (x-1)-2
Like I said, the second one may not be right.

Answer 4

Do you mean 16-x^2?

Why it's (4-x)*(4+x).

Multiplying the two:
16-4x+4x-x^2 = 16-x^2

or are you wondering what an exponent is?

x^2 = x*x
x^3 = x*x*x

Get it?

Answer 5

x times x
a little 3 would be x times x times x