Question

5x(3 la puterea 2002-3 la puterera 2001-9 la puterea 1000) cat face ?

Answer 1

5 x ( 3^2002 - 3^2001 - 9^1000) =

5 x (3^2002 - 3^2001 - (3^2)^1000) =

5 x (3^2002 - 3^2001 - 3^2000) =

5 x 3^2000 x (3^2 - 3^1 - 1) =

5 x 3^2000 x (9 - 3 - 1) =

5 x 3^2000 x 5 =

5^2 x 3^2000 =

25 x 3^2000

Answer 2

5x(3²⁰⁰²-3²⁰⁰¹-9¹⁰⁰⁰) = 5x(3²⁰⁰²-3²⁰⁰¹-3²ˣ¹⁰⁰⁰) = 5x3²⁰⁰⁰x(3²-3¹-3⁰) =

=5x3²⁰⁰⁰x(9-3-1) = 5x3²⁰⁰⁰x5 = 5²x3²⁰⁰⁰ = (5x3¹⁰⁰⁰)² = patrat perfect.