Explicație pas cu pas:
a)
[tex]A = {5}^{2n + 1} \cdot {4}^{3n + 2} + {10}^{2n + 1} \cdot {2}^{4n + 1} = {5}^{2n + 1} \cdot {4}^{2n} \cdot {4}^{n + 2} + {10}^{2n + 1} \cdot 2 \cdot {2}^{4n} = \\ = {5}^{2n + 1} \cdot {4}^{2n} \cdot {2}^{2n + 4} + 2 \cdot {10}^{2n + 1} \cdot {4}^{2n} = {5}^{2n + 1} \cdot {4}^{2n} \cdot {2}^{3} \cdot {2}^{2n + 1} + 2 \cdot {10}^{2n + 1} \cdot {4}^{2n} \\ = {10}^{2n + 1} \cdot {4}^{2n} \cdot (8 + 2) = {10}^{2n + 1} \cdot {4}^{2n} \cdot 10 = {10}^{2n + 2} \cdot {4}^{2n} = {10}^{2(n + 1)} \cdot {4}^{2n} \\ = \bf {({4}^{n} \cdot {10}^{n + 1})}^{2} [/tex]
b)
[tex]A = {10}^{2n + 2} \cdot {4}^{2n} = {10}^{2n + 2} \cdot {2}^{4n} = {10}^{2} \cdot {10}^{2n} \cdot 2 \cdot {2}^{4n - 1} = \\ = 200 \cdot {10}^{2n} \cdot {2}^{4n - 1} \red{ \bf \ \vdots \: 200}[/tex]
q.e.d.
