Cách làm cho bạn:
Ta có:
$A_{n}^{2}+2C_{n}^{1}=30$
<=> $\frac{n!}{(n-2)!}+2\frac{n!}{1!(n-1)!}=30$
<=> $\frac{n(n-1)(n-2)!}{(n-2)!}+2\frac{n(n-1)!}{(n-1)!}=30$
⇔ n(n – 1) + 2n = 30
⇔ $n^{2} + n – 30 = 0$
⇔ n = 5 (thỏa mãn) hoặc n = – 6 (loại).
=> n = 5.
$(3x – 2)^{n} = (3x – 2)^{5} = [3x + (– 2)^{5}]$
$=C_{5}^{0}. (3x)^{5}+C_{5}^{1}. (3x)^{4}. (-2)+C_{5}^{2}.(3x)^{3}. (-2)^{2}+C_{5}^{3}. (3x)^{2}. (-2)^{3}+C_{5}^{4}. (3x)^{1}. (-2)^{4}+C_{5}^{5}. (-2)^{5}$
= $243x^{5}– 810x^{4} + 1 080x^{3} – 720x^{2} + 240x – 32.$
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