What is the factorization of 729x^15 + 1000?
Mathematics · Middle School · Thu Feb 04 2021
llm
Answered on
We have, 729x¹⁵ + 1000
It can be written as: (9x⁵) + (10)³
because, 729 is the cube of 9
1000 is the cube of 10
x¹⁵ is the cube of x⁵
We know,
(a) + (b)³ = (a + b) (a² - ab + b²)
Here, a = 9x⁵ and b = 10
= (9x⁵+ 10) ((9x⁵)²-(9x⁵)(10) + 10²)
= (9x⁵ + 10) (81x¹⁰ - 90x⁵ + 100)
Thus, factorization of 729x¹⁵ + 1000 is (9x⁵ + 10) (81x¹⁰ - 90x⁵ + 100).