Divide $81 x^{3} (50 x^{2} - 98)$ by $27 x^{2} (5 x + 7)$

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Solution

$\frac{81 x^{3} (50 x^{2} - 98)}{27 x^{2} (5 x + 7)}$
Separate the numerator and denominator in two expressions,
$\Rightarrow \frac{81 x^{3} (25 x^{2} - 49) 2}{27 x^{2} (5 x + 7)} = \frac{3.2 ({(5 x)}^{2} - {(7)}^{2})}{(5 x + 7)}$

Using ${(a)}^{2} - {(b)}^{2} = (a + b) (a - b)$

$\Rightarrow \frac{6 (5 x + 7) (5 x - 7)}{(5 x + 7)} = 6 (5 x - 7) = 30 x - 42$
Hence, the answer is $30 x - 42.$

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