(3 - 4\(\sqrt{2}\))(1 + 3\(\sqrt{2}\)) = a + b\(\sqrt{2}\),

3 + 9\(\sqrt{2} - 4\sqrt{2} - (4\sqrt{2} \times 3\sqrt{2}) = a + b\sqrt{2}\)

3 + 5\(\sqrt{2} - (4 \times 3\sqrt{2} \times \sqrt{2}) = a + b\sqrt{2}\)

3 + 5\(\sqrt{2} - (12 \times 2) = a + b\sqrt{2}\)

3 + 5\(\sqrt{2} - 24 = a + b\sqrt{2}\)

-21 + 5\(\sqrt{2}\) = a + b\(\sqrt{2}\)

Comparing both sides, we have b = 5