Factorise $343 y^{3} - 1000$ using the above results

(7 y - 10) (7 y^{2} + 70 y + 100)

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(7 y - 10) (49 y^{2} + 70 y + 10)

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(7 y - 10) (49 y^{2} + 70 y + 100)

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None of the above

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Solution

The correct option is C $(7 y - 10) (49 y^{2} + 70 y + 100)$
$343 y^{3} - 1000$ $=$ $(7 y)^{3} - (10)^{3}$
We know that $x^{3} - y^{3} = (x - y) (x^{2} + x y + y^{2})$
Comparing both sides, then we have
$x = 7 y$ and $y = 10$
Therefore, value of $(7 y)^{3} - (10)^{3}$ is
$= (7 y - 10) [(7 y)^{2} + (7 y) (10) + (10)^{2}]$
$=$ $(7 y - 10) (49 y^{2} + 70 y + 100)$

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Factorise the quadratic polynomial by splitting the middle term: y² - 4 y –21

y^{2} + 7 y - 144

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