Factors for $a^{2} b^{2} + c^{2} d^{2} - a^{2} c^{2} - b^{2} d^{2}$ are:

(a + d) (a - d) (b + c) (b - c)

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(a^{2} - b^{2})

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(a^{2} - d^{2}) (b^{2} - c^{2})

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None of these

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Solution

The correct option is A $(a + d) (a - d) (b + c) (b - c)$
$a^{2} b^{2} + c^{2} d^{2} - a^{2} c^{2} - b^{2} d^{2}$
$= a^{2} b^{2} - a^{2} c^{2} - b^{2} d^{2} + c^{2} d^{2}$
$= a^{2} (b^{2} - c^{2}) - d^{2} (b^{2} - c^{2})$
$= (a^{2} - d^{2}) (b^{2} - c^{2})$
$= (a + d) (a - d) (b + c) (b - c)$

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Similar questions

a^{2} b^{2} + c^{2} d^{2} - a^{2} c^{2} - b^{2} d^{2}

\frac{a^{2} - b^{2} - c^{2}}{(a - b) (a - c)} + \frac{b^{2} - c^{2} - a^{2}}{(b - c) (b - a)} + \frac{c^{2} - a^{2} - b^{2}}{(c - a) (c - b)}

∣ ∣ ∣ ∣ ∣ \begin{matrix} - a^{2} & a b & a c a b & - b^{2} & b c a c & b c & - c^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣ + ∣ ∣ ∣ ∣ ∣ \begin{matrix} a^{2} & - b^{2} & - c^{2} - a^{2} & b^{2} & - c^{2} - a^{2} & - b^{2} & c^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣ =

a, b, c, d, e

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\pm \sqrt{a^{2} + b^{2} + c^{2}}

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