Coefficient of x in (1+x)p(1−x)q ‌pC0‌qC1+‌pC1‌qC0=−3⇒p−q=−3 Coefficient of x2 in (1+x)p(1−x)q ‌pC0‌qC2−‌pC1‌qC1+‌pC2‌qC0=−5 ‌
q(q−1)
2
−pq+‌
p(q−1)
2
=−5 ‌
q2−q
2
−(q−3)q+‌
(q−3)(q−4)
2
=−5 ⇒q=11,p=8 Coefficient of x3 in (1+x)8(1−x)11 =−‌11C3+‌8C1‌11C2−‌8C2‌11C1+‌8C3=23