<s>[INST] Finding product without working it out What's the easy way to find the solution for the below problem without actually multiplying the numbers:
$$(24 * 24) - (16 * 16)?$$
I tried multiplying the numbers but that is a long way.
The answer is in the below format
A) $(8 \times 8)$
B) $(40 \times 40)$ 
C) $(8 \times 2)$ 
D) $(8 \times 40)$
 [/INST] You can also try and use prime factorization:
\begin{align}(24 \cdot 24) - (16 \cdot 16) &= 24^2 - 16^2 \\ &= (3\cdot 2^3)^2 - (2^4)^2 \\ &= (3^2 \cdot2^6) - (2^8) \\ &= 2^6 \bigg[3^2 - 2^2 \bigg] \\ &= 2^6 \bigg[9 - 4 \bigg] \\ &= 2^6 (5) \\ &= 64(5) \\ &= 320\end{align}
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