The expanded form of 9578 is
\(9\times10000+5\times1000+7\times10+8\times1\)
\(9\times1000+5\times100+7\times10+8\times1\)
\(9\times1000+57\times10+8\times1\)
\(9\times100+5\times100+7\times10+8\times1\)
Let's break the number 9578 into each digit and its place value in simple steps.
Write the digits: 9, 5, 7, 8.
From left to right:
9 is in the thousands place: \(9 \times 1000 = 9000\).
5 is in the hundreds place: \(5 \times 100 = 500\).
7 is in the tens place: \(7 \times 10 = 70\).
8 is in the ones place: \(8 \times 1 = 8\).
Now add these parts step by step:
\(9000 + 500 = 9500\).
\(9500 + 70 = 9570\).
\(9570 + 8 = 9578\).
So the expanded form is:
\(9\times1000 + 5\times100 + 7\times10 + 8\times1\).
That matches option B.