Question 62

How much is $y^{4} - 12 y^{2} + y + 14$ greater than $17 y^{3} + 34 y^{2} - 51 y + 68$ ?

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Solution

Required expression is
$y^{4} - 12 y^{2} + y + 14 - (17 y^{3} + 34 y^{2} - 51 y + 68) = y^{4} - 12 y^{2} + y + 14 - 17 y^{3} - 34 y^{2} + 51 y - 68$
On combining the like terms.
$= y^{4} - 12 y^{2} - 34 y^{2} + y + 51 y + 14 - 68 - 17 y^{3} = y^{4} - 46 y^{2} + 52 y - 17 y^{3} - 54 = y^{4} - 17 y^{3} - 46 y^{2} + 52 y - 54$
So, $y^{4} - 12 y^{2} + y + 14$ is $y^{4} - 17 y^{3} - 46 y^{2} + 52 y - 54$ greater than $17 y^{3} + 34 y^{2} - 51 y + 68.$

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