Which expansion is correct for ( (10-3)^2 )?

Correct answer: (10^2-2\cdot10\cdot3+3^2)

The direct answer is option C. Let x=10 and y=3. The identity for a difference squared is (x-y)^2=x^2-2xy+y^2. Therefore (10-3)^2=10^2-2×10×3+3^2=100-60+9=49. Option A uses a plus middle term, so it represents (10+3)^2, not a difference. Option B is the difference of squares, 10^2-3^2, which equals (10-3)(10+3), not the square of 10-3. Option C has the correct negative middle term and positive final square. Option D omits the middle term entirely, so it is incomplete. Remember: in a squared subtraction, the middle term is negative, but the last square remains positive.