Given, (2.5p−1.5q)2−(1.5p−2.5q)2.
We know, (a−b)2=a2−2ab+b2.
Then,
(2.5p−1.5q)2−(1.5p−2.5q)2
=[(2.5p)2−2(2.5p)(1.5q)+(1.5q)2]−[(1.5p)2−2(1.5p)(2.5q)+(2.5q)2]
=6.25p2−7.5pq+2.25q2−2.25p2+7.5pq−6.25q2
=6.25p2+2.25q2−2.25p2−6.25q2
=6.25p2−2.25p2+2.25q2−6.25q2
=4p2−4q2.
Therefore, option A is correct.