Factor completely x8 − 625. (x4 − 25)(x4 + 25) (x2 − 5)(x2 + 5)(x4 − 25) (x2 − 5)(x2 − 5)(x4 − 25) (x2 − 5)(x2 + 5)(x4 + 25)
Mathematics · Middle School · Thu Feb 04 2021
Answered on
Given:
(x^8 - 625)
Factor completely.
Solution:
The given equation is an example of the difference between two binomials, hence the factor that satisfies the condition is based from the equation.
(a^2 - b^2) = (a + b)(a - b)
(x^8 - 625)= (x^4 + 25)(x^4 - 25)
In order to check if the equation is true, we used the FOIL method. Multiply the first term of the first equation, to the first and last term of the second equation. Then, multiply the last term of the first equation, to the first and last term of the second equation.
To clearly see how it works, here's a step by step solution.
= (x^4)(x^4)
=x^8
First term of the first equation multiplied to the first term of the second equation.
=(x^4)(-25)
= -25x^4
First term of the first equation multiplied to the last term of the second equation.
=(25)(x^4)
=25x^4
Last term of the first equation multiplied to the first term of the second equation.
=(25)(-25)
= -625
Last term of the first equation multiplied to the fast term of the second equation.
= x^8 - 25x + 25x - 625
= x^8 - 625
Final answer:
(x^8 - 625)= (x^4 + 25)(x^4 - 25)