Question : What is the LCM of $(8 x^{3} + 80 x^{2} + 200 x)$ and $(4 x^{4} + 16 x^{3} - 20 x^{2})$ ?
Option 1: $8 x^{2} (x + 5)^{2} (x - 1)$
Option 2: $8 x^{2} (x - 1)^{2} (x + 5)$
Option 3: $4 x^{2} (x - 1)^{2} (x + 5)$
Option 4: $4 x^{2} (x + 5)^{2} (x - 1)$

Question

Question : Simplify: $\frac{256 x^{4} - 16 y^{4}}{(80 x^{2} - 20 y^{2}) (16 x^{2} + 4 y^{2})}$

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Answer 1

Correct Answer: $8 x^{2} (x + 5)^{2} (x - 1)$

Solution : Consider, $(8 x^{3} + 80 x^{2} + 200 x)$
Taking $8 x$ as common, we get,
$= 8 x (x^{2} + 10 x + 25)$
$= 8 x (x^{2} + 5 x + 5 x + 25)$
$= 8 x (x (x + 5) + 5 (x + 5))$
$= 8 x (x + 5)^{2}$
Now consider, $(4 x^{4} + 16 x^{3} - 20 x^{2})$
Taking $4 x^{2}$ as common, we get,
$= 4 x^{2} (x^{2} + 4 x - 5)$
$= 4 x^{2} (x^{2} - x + 5 x - 5)$
$= 4 x^{2} (x (x - 1) + 5 (x - 1))$
$= 4 x^{2} (x - 1) (x + 5)$
$∴$ LCM $= 8 x^{2} (x + 5)^{2} (x - 1)$
Hence, the correct answer is $8 x^{2} (x + 5)^{2} (x - 1)$ .

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Question : What is the LCM of (8x3+80x2+200x) and (4x4+16x3−20x2)?Option 1: 8x2(x+5)2(x−1)Option 2: 8x2(x−1)2(x+5)Option 3: 4x2(x−1)2(x+5)Option 4: 4x2(x+5)2(x−1)

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Question : What is the LCM of $(8 x^{3} + 80 x^{2} + 200 x)$ and $(4 x^{4} + 16 x^{3} - 20 x^{2})$ ?
Option 1: $8 x^{2} (x + 5)^{2} (x - 1)$
Option 2: $8 x^{2} (x - 1)^{2} (x + 5)$
Option 3: $4 x^{2} (x - 1)^{2} (x + 5)$
Option 4: $4 x^{2} (x + 5)^{2} (x - 1)$