Question

Calculeaza folosind factorul comun: c) 5^n+2+5^n+1 - 5^n; d) 2^n+2×3^n+1-6n,e urgent!!!​

Answer 1

Explicație pas cu pas:

${5}^{n + 2} + {5}^{n + 1} - {5}^{n} = {5}^{n} \cdot ( {5}^{2} + 5 - 1) = {5}^{n} \cdot (25 + 4) = 29 \cdot {5}^{n}$

${2}^{n + 2} \cdot {3}^{n + 1} - {6}^{n} = {2}^{2} \cdot {2}^{n} \cdot 3 \cdot {3}^{n} - {6}^{n} = 12 \cdot {(2 \cdot 3)}^{n} - {6}^{n} = 12 \cdot {6}^{n} - {6}^{n} = {6}^{n} \cdot (12 - 1) = 11 \cdot {6}^{n}$

Answer 2

Răspuns:

Explicație pas cu pas:

c) 5^n(5²+5-1)=5^n(25+5-1)=29·5^n

d)2^(n+2)·3^(n+1)-6^n=2^n·3^n(2²·3-1)=11·6^n