(1 + 2a)^{4}

= 1 + ^{4}C_{1}.2a + ^{4}C_{2}.(2a)^{2} + ^{4}C_{3}.(2a)^{3} + (2a)^{4}

= 1 + 8a + 24a^{2} + 32a^{3} + 16a^{4} ..... (1)

Again,

(2 - a)^{5}

= 2^{5} - ^{5}C_{1}.2^{4}.a + ^{5}C_{2}.2^{3}.a^{2} - ^{5}C_{3}.2^{2}.a^{3} + ^{5}C_{4}.2.a^{4 }- ^{}a^{5}

=32 - 80a + 80a^{2} - 40a^{3} +10a^{4} - a^{5}

Now,

(1 + 2a)^{4} (2 - a)^{5}

= [1 + 8a + 24a^{2} + 32a^{3 }+ 16a^{4}].[32 - 80a + 80a^{2} - 40a^{3 }+ 10a^{4} - a^{5}]

Required coefficient of a^{4} in the product

= 1 × 10 + 8 × (-40) + 24 × 80 + 32 × (-80) + 16 × 32

= -438