(1+2a)4 ..(1)
(2−a)5..(2)
Coefficient of a4 term can be obtained when term a from(1) and a4 from(2) are multiplied.so combining all these coefficints we can find the coefficint of a4 in given expansion,thus we get,
coeeficient of a4 will be (taking 1 and 2 in equation)
(a01×a42)+(a11×a32)+(a21×a22)+(a31×a12)+(a41×a02)
[4C0×(1)4(2a)2×5C4×21×(−a)5−1]+[4C1×(1)3(2a)1×5C3×22×(−a)3]+[4C2×(1)2(2a)2×5C2×23×(−a)2]+[4C3×(1)1(2a)3×5C1×24×(−a)1]+[4C4×(1)0(2a)4×5C0×25×(−a)0]
10a4−320a4+1920a4−2560a4+512a4
−438a4
Therefore coeffcient of a4 is −438