# Help with $7 · 7^{k+2} + 64 · 8^{2k+1}$=$7(7^{k+2} + 8^{2k+1}) + 57 · 8^{2k+1}.$

Could someone please explain why 7 is being subtracted from 64 in:

$7 · 7^{k+2} + 64 · 8^{2k+1}$ to make

$7(7^{k+2} + 8^{2k+1}) + 57 · 8^{2k+1}.$

Also, how does $7^{k+2}$ get factored by 7 to make the same thing.

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Note that $64=57+7$, so $$64\cdot8^{2k+1}=7\cdot8^{2k+1}+57\cdot8^{2k+1}$$
Your problem now becomes $$7\cdot7^{k+2}+7\cdot8^{2k+1}+57\cdot8^{2k+1}=7(7^{k+2}+8^{2k+1})+57\cdot8^{2k+1}$$