( $q^{2}$ *$c^{2}$* $a^{2}$* $p^{2}$- $q^{2}$* $a^{4}$*$c^{2}$)/ ($c^{4}$* $a^{4}$* $p^{2}$)
You asked:
Evaluate the expression: \(\frac{{q}^{2} {c}^{2} {a}^{2} {p}^{2} - {q}^{2} {a}^{4} {c}^{2}}{{c}^{4} {a}^{4} {p}^{2}}\)
MathBot Answer:
Evaluated
\(\displaystyle \frac{{q}^{2} {c}^{2} {a}^{2} {p}^{2} - {q}^{2} {a}^{4} {c}^{2}}{{c}^{4} {a}^{4} {p}^{2}} = \frac{- a^{4} c^{2} q^{2} + a^{2} c^{2} p^{2} q^{2}}{a^{4} c^{4} p^{2}} \)
Expanded
\[\frac{{q}^{2} {c}^{2} {a}^{2} {p}^{2} - {q}^{2} {a}^{4} {c}^{2}}{{c}^{4} {a}^{4} {p}^{2}} = - \frac{q^{2}}{c^{2} p^{2}} + \frac{q^{2}}{a^{2} c^{2}}\]
Factored
\[\frac{{q}^{2} {c}^{2} {a}^{2} {p}^{2} - {q}^{2} {a}^{4} {c}^{2}}{{c}^{4} {a}^{4} {p}^{2}} = - \frac{q^{2} \left(a - p\right) \left(a + p\right)}{a^{2} c^{2} p^{2}}\]