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B
x(1+2y)(1+2y+4y2)
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C
x(1−2y)(1−2y+4y2)
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D
x(1+2y)(1−2y+4y2)
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Solution
The correct option is Bx(1−2y)(1+2y+4y2) Formula used:a3−b3=(a−b)(a2+ab+b2) Given, x−8xy3=x(1−8y3) =x[13−(2y)3] =x[(1−2y)(12+1×2y+(2y)2)] =x(1−2y)(1+2y+4y2) Hence, Option A is correct.