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Factorize completely 8a + 125ax3
...

Factorize completely 8a + 125ax3

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)

View answer & explanation

Correct answer is B

$8a + 125ax^{3} = (2^{3})a + 5^{3} ax^{3}$

= $a(2^3 + 5^3 x^3)$

∴ $a[2^3 + (5x)^3]$

$a^3 + b^3 = (a + b)(a^2 - ab + b^2)$

∴ $a(2^3 + (5x)^3)$

= $a(2 + 5x)(4 - 10x + 25x^2)$

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