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Factorize completely 8a + 125ax\(^3\)

Mathematics
JAMB 1986

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)
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Correct Answer: Option B
Explanation

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

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

∴\(a[2^3 + (5x)^3]\)

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

∴ \(a(2^3 + (5x)^3)\)

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


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