What is the complete simplified form of ( (x+5)^3-(x-5)^3 )?

Correct answer: (30x^2+250)

The direct answer is option A: \(30x^2+250\). Expand both cubes carefully. Using \((x+5)^3=x^3+15x^2+75x+125\), and \((x-5)^3=x^3-15x^2+75x-125\), subtract the second expression from the first: \(x^3-x^3=0\), \(15x^2-(-15x^2)=30x^2\), \(75x-75x=0\), and \(125-(-125)=250\). Therefore the result is \(30x^2+250\). Option A is correct because it contains the surviving square and constant terms. Option B, \(30x^2+50x+250\), is wrong because the linear terms are actually equal and cancel; no \(x\) term remains. Option C incorrectly leaves a cubic term and uses an incorrect coefficient. Option D gives only the constant part and omits \(30x^2\). A useful check is that replacing \(x o -x\) changes the original expression to its negative, so the result should contain only odd-power behaviour overall; because the difference is arranged with the shifts, the calculated expression confirms the expansion directly. Exam cue: expand signs carefully, especially when subtracting the entire second bracket.