Question

Study the pattern:
$$1\times 8+1=9$$

$$1234\times 8+4=9876$$

$$12\times 8+2=98$$

$$12345\times 8+5=98765$$
$$123\times 8+3=987$$
Write the next two steps. Can you say how the pattern works?

Answer 1

$$123456\times 8+6=987648+6=987654$$
$$1234567\times 8+7=9876536+7=9876543$$
Yes, the pattern works.
As $$123456=111111+11111+1111+111+11+1$$,
$$123456\times 8=(111111+11111+1111+111+11+1)\times 8$$
$$=111111\times 8+11111\times 8+1111\times 8+111\times 8+11\times 8+1\times 8$$
$$=888888+88888+8888+888+88=8=987648$$
$$123456\times 8+6=987648+6=987648$$.