Factorize completely 8a + 125ax\(^3\)
A
(2a + 5x2)(4 + 26ax)
B
a(2 + 5x)(4 - 10x + 25x2)
C
(2a + 5x)(4 - 10ax + 25x2)
D
a(2 + 5x)(4 + 10ax + 25x2)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
\(8a + 125ax^{3} = (2^{3})a + 5^{3} ax^{3}\)
= \(a(2^3 + 5^3 x^3)\)
∴\(a[2^3 + (5x)^3]\)
\(a^3 + b^3 = (a + b)(a^2 - ab + b^2)\)
∴ \(a(2^3 + (5x)^3)\)
= \(a(2 + 5x)(4 - 10x + 25x^2)\)
Source: Myschool Past Questions Archive (Record #32076)