the question is: Factor the following: x(to the second power) -100?

Question

I dont just want the answer I need to know how to do it

and x(to the 3rd power) + w(to the 3rd power)

Answer 1

1) x^2 - 100 = (x + a)(x + b)
2) No "x" on left side, so a = -b:
3) x^2 - 100 = (x - b)(x + b), multiply right side:
4) x^2 - 100 = x^2 - b^2, subtract x^2:
5) -100 = - b^2, multiply both sides by -1:
6) 100 = b^2, take square root of both sides:
7) b= 10, a = -10, substitute a and b:

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

Answer 2

The factors are the two things that multiplied together give that answer. All of the things that are in that form have the same style of answer. They are always (x + number) and (x - same number) where the number to use is the square root of the original number. In your example with 100 use the number 10 because 10x10 = 100.
When you multiply it out you get: x times x plus 10x minus 10x plus +10 times -10. The x times x is x(to the second power). Since the plus 10x and the minus 10x cancel each other there are no x terms left. Multiplying the +10 times -10 gives the -100 you want. You are then left with x(to the second power) -100.

Answer 3

Well... this is the problem of factorizing the substitution of two squares of numbers. By type: x^2-y^2=?
There is a type, who told us that x^2-y^2=(x-y)*(x+y). You can proof this type by many ways. In your case, y^2=100. So, x^2-100=(x-10)*(x+10).
Generally, if you have a polynomial of second degree, let P(x) and you find the solutions of it, meaning P(x)=a*x^2+b*x+c=0, (so x1,2=(-b±√(b^2-4*a*c))/(2*a)) then you can factorize the polynomial as: P(x)=(x-x1)*(x-x2).
So, by using this equation, you can factorize the equation as: x^3+w^3=(x+w)*(x^2-x*w+w^2). Then you can factorize the (x^2-w*x+w^2) by the way I told you in the prior paragraph.

Answer 4

Since 100 = 10²
x² - 100 = x² - 10²
x² - 10² = ( x + 10 )( X - 10 )

As for the equation, x³ + w³ (Use the Factor Theorem)
Let f(x) = x³ + w³
f(-w) = (-w)³ + w³
= 0
Therefore (x + w) is a factor of f(x)
Hence,
x³ + w³ = (x + w)(x² - wx + w²)

Answer 5

This is the different of two squares.

The formula for difference of two squares is:

x^2 - y^2 = (x + y)(x - y)

In your problem, the first term is the square of x and the second term is the square of 10

Therefore, (x + 10)(x - 10) is the factor form

Answer 6

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

x^3 + w^3 = (x + w)(x^2 - xw + w^2)

Answer 7

X(second power) - 100
= (x)(x)-(10)(10)
=x (power2) - 10(power2)

Is this hint enough??

Answer 8

it won't help you learn if you ask us for the answer i know it it's pretty easy