Question 58 (d)

Subtract:

$x^{4} + 3 x^{3} y^{3} + 5 y^{4}$ from $2 x^{4} - x^{3} y^{3} + 7 y^{4} .$

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Solution

We have,
$2 x^{4} - x^{3} y^{3} + 7 y^{4} - (x^{4} + 3 x^{3} y^{3} + 5 y^{4}) = 2 x^{4} - x^{3} y^{3} + 7 y^{4} - x^{4} - 3 x^{3} y^{3} - 5 y^{4}$
On combining the like terms,
$= 2 x^{4} - x^{4} - x^{3} y^{3} - 3 x^{3} y^{3} + 7 y^{4} - 5 y^{4} = x^{4} - 4 x^{3} y^{3} + 2 y^{4}$

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(3 y^{8} - 4 y^{6} + 5 y^{4}) \div y^{4}

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(5 x^{4} + 7 y^{4}) : (5 x^{4} - 7 y^{4})

Divide the given polynomial by the given monomial
$(3 y^{8} - 4 y^{6} + 5 y^{4}) \div y^{4}$

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