( q2q^{2} *c2c^{2}* a2a^{2}* p2p^{2}- q2q^{2}* a4a^{4}*c2c^{2})/ (c4c^{4}* a4a^{4}* p2p^{2})

asked by guest
on Jan 14, 2025 at 2:45 pm



You asked:

Evaluate the expression: q2c2a2p2−q2a4c2c4a4p2\frac{{q}^{2} {c}^{2} {a}^{2} {p}^{2} - {q}^{2} {a}^{4} {c}^{2}}{{c}^{4} {a}^{4} {p}^{2}}

MathBot Answer:

Evaluated



q2c2a2p2−q2a4c2c4a4p2=−a4c2q2+a2c2p2q2a4c4p2\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

q2c2a2p2−q2a4c2c4a4p2=−q2c2p2+q2a2c2\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

q2c2a2p2−q2a4c2c4a4p2=−q2(a−p)(a+p)a2c2p2\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}}

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