Which is the correct expansion in the area model of a square with side \(10-3\)?

Correct answer: \(100-60+9\)

The direct answer is option B. The square has side \(10-3\), so its area is \((10-3)^2\). Use the identity \((a-b)^2=a^2-2ab+b^2\), with \(a=10\) and \(b=3\). This gives \(10^2-2(10)(3)+3^2=100-60+9\). The value is also \(49\), which agrees with \(7^2\). Option A, \(100-9\), is the difference of two squares, not the square of a difference. Option C has the wrong sign for the middle term; it belongs to a sum pattern. Option D uses \(30\) instead of \(60\), because it forgets the factor 2 in \(2ab\). A useful check is to calculate the side first: \(10-3=7\), so the area must be 49.