Grade 9 Factoring Fully?

Question

Hi, my question is:
x 4 (x to the fourth power) - 625
x4-625

I jsut dont get how to factor fully. Thanks.

Answer 1

First, show your powers by use of the "^"

The point here is to think outside the "box". The box is something like x^2-25, which you should identify as (x-5)(x+5).

So x^4 can be looked upon as (x^2)^2, and the expression as (x^2)^2-625, which gives you
(x^2-25)(x^2+25). As shown above, you can again factor x^2-25.

Answer 2

x^4 - 625
In this problem, 625 is the 4th power of 5, ie. 5^4 = 625. So the equation can be rewritten as:
= x^4 - 5^4
= (x²)² - (5²)²
This is in the form of the identity (a² - b²) & can be expanded as: (a+b)(a-b)
Similarly,
(x²)² - (5²)² = (x² + 5²) (x² - 5²)
But, (x² - 5²) is same as (a² - b²) & can be expanded
......"...........= (x² + 5²) (x + 5) (x - 5)
.......................==================
But, (x² + 5²) = (x + 5)² - 10x. So, the above answer can also be written as :
(x^4 - 5^4) = (x²)² - (5²)² = {(x+5)²- 10x} (x + 5) (x - 5)
...................... ................ ======================

Answer 3

x^4-625 = x^4 - 5^4
Now use the identity
a^2-b^2 = (a+b)(a-b)

x^4-5^4 = (x^2+5^2)(x^2-5^2)
= (x^2+25)(x^2-5^2)
use the same identity again on the factor having terms related by minus sign.

=(x^2+25)(x^+5)(x-5)
the three required factors

Answer 4

remember that a2-b2=(a-b)(a+b)...
and that x4=(x2)2... and 625=(25)^2
so x4-625
=(x2 - 25)(x2 + 25)
And the first part can be factored even more.
(x-5)(x+5)(x^2+25)... remember, (x^2+25) isn't equal to (x+5)^2
Your answer is (x-5)(x+5)(x^2+25)

Answer 5

x⁴-625 = (x²-25)(x²+25)

Answer 6

(x2 +25)(x2-25) Now, the second () show the difference of two perfect squares, so continue.

(x2+25)(x+5)(x-5)

Answer 7

[12]
x^4-625
=(x^2)^2-(25)^2
=(x^2-25)(x^2+25)
={(x)^2-(5)^2}(x^2+25)
=(x-5)(x+5)(x^2+25)