What is ((5r^7)/6+(p^4q)/7)((p^4q)/7-(5r^7)/6) ?

The solution to ((5r^7)/6+(p^4q)/7)((p^4q)/7-(5r^7)/6) is ((35r^7+6p^4q)(6p^4q-35r^7))/(1764)

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simplify ((5r^7)/6+(p^4q)/7)((p^4q)/7-(5r^7)/6)

simplify

(\frac{5 r ^{7}}{6} + \frac{p ^{4} q}{7}) (\frac{p ^{4} q}{7} - \frac{5 r ^{7}}{6})

\frac{( 35 r ^{7} + 6 p ^{4} q ) ( 6 p ^{4} q - 35 r ^{7} )}{1764}

Solution steps

(\frac{5 r ^{7}}{6} + \frac{p ^{4} q}{7}) (\frac{p ^{4} q}{7} - \frac{5 r ^{7}}{6})

Simplify

\frac{5 r ^{7}}{6} + \frac{p ^{4} q}{7} : \frac{35 r ^{7} + 6 p ^{4} q}{42}

= \frac{35 r ^{7} + 6 p ^{4} q}{42} (\frac{p ^{4} q}{7} - \frac{5 r ^{7}}{6})

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{( 35 r ^{7} + 6 p ^{4} q ) ( \frac{p ^{4} q}{7} - \frac{5 r ^{7}}{6} )}{42}

Simplify

(35 r^{7} + 6 p^{4} q) (\frac{p ^{4} q}{7} - \frac{5 r ^{7}}{6}) : \frac{( 35 r ^{7} + 6 p ^{4} q ) ( p ^{4} q \cdot 6 - 35 r ^{7} )}{42}

= \frac{\frac{( 35 r ^{7} + 6 p ^{4} q ) ( p ^{4} q \cdot 6 - 35 r ^{7} )}{42}}{42}

Apply the fraction rule:

\frac{\frac{a}{b}}{c} = \frac{a}{b \cdot c}

= \frac{( 35 r ^{7} + 6 p ^{4} q ) ( p ^{4} q \cdot 6 - 35 r ^{7} )}{42 \cdot 42}

Multiply the numbers:

42 \cdot 42 = 1764

= \frac{( 35 r ^{7} + 6 p ^{4} q ) ( p ^{4} q \cdot 6 - 35 r ^{7} )}{1764}

= \frac{( 35 r ^{7} + 6 p ^{4} q ) ( 6 p ^{4} q - 35 r ^{7} )}{1764}

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What is ((5r^7)/6+(p^4q)/7)((p^4q)/7-(5r^7)/6) ?
The solution to ((5r^7)/6+(p^4q)/7)((p^4q)/7-(5r^7)/6) is ((35r^7+6p^4q)(6p^4q-35r^7))/(1764)