96𝑎𝑏𝑐(3𝑎−12)(5𝑏−30)÷144(𝑎−4)(𝑏−6) =96𝑎𝑏𝑐(3𝑎−12)(5𝑏−30)144(𝑎−4)(𝑏−6) =4×2×12×𝑎𝑏𝑐×3×(𝑎−4)×5×(𝑏−6) 12×12×(𝑎−4)×(𝑏−6) =2×𝑎𝑏𝑐×5 =10𝑎𝑏𝑐 ...

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Number of Elements in a Cartesian Product

96𝑎𝑏𝑐3𝑎−1...

Question

$96 a b c (3 a - 12) (5 b - 30) \div 144 (a - 4) (b - 6) =__________$

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Solution

$96 a b c (3 a - 12) (5 b - 30) \div 144 (a - 4) (b - 6) = \frac{96 a b c (3 a - 12) (5 b - 30)}{144 (a - 4) (b - 6)} = \frac{4 \times 2 \times 12 \times a b c \times 3 \times (a - 4) \times 5 \times (b - 6)}{12 \times 12 \times (a - 4) \times (b - 6)} = 2 \times a b c \times 5 = 10 a b c$

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