Find the coefficient of (x ^ 2 + 3x + 2) ^ 5 expansion with X term Ask for a magic hand

Find the coefficient of (x ^ 2 + 3x + 2) ^ 5 expansion with X term Ask for a magic hand

(x＋3x＋2)^5=[(x＋1)(x＋2)]^5=(x＋1)^5(x＋2)^5
Then the coefficient with X term in the expansion is the product (5) × (2 ^ 5) = 160 of the first term coefficient C (4,5) in (x + 1) ^ 5 expansion and the constant term 2 ^ 5 in (x + 2) ^ 5 expansion, plus the product of the first term coefficient (2 ^ 4) × C (4,5) = 80 in (x + 1) ^ 5 expansion and the constant term 1 in (x + 1) ^ 5 expansion. In the final expansion, the first term is (160 + 80) x = 240x