Question

Scrieti urmatoarele numere sub forma de produs utilizand factorul comun:
a) 2 la puterea 76+2 la puterea 78+2 la puterea 80
b) 3×5^47+2×5^48+6×5^49
c) 13^14×-13^13×2-13^12
dau coroana ^ inseamna la puterea

Answer 1

a)2^76(2²+2^4)=2^76 (4+16)=20*2^76

b)5^47(3-2*5+6*5²)=(3-10+150)*5^47=143*5^47

c)13^12(13²-2*13-1)=(169-26-1)*13^12=142*13^12

Answer 2

a)   2⁷⁶ + 2⁷⁸ + 2⁸⁰ = 2⁷⁶ x ( 1 + 2² + 2⁴ ) = 2⁷⁶ x ( 1 + 4 + 16 ) = 2⁷⁶ x 21

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b)   3 x 5⁴⁷ + 2 x 5⁴⁸ + 6 x 5⁴⁹ = 5⁴⁷ x  163

= 5⁴⁷ x ( 3 + 2 x 5 + 6 x 5² ) =

= 5⁴⁷ x ( 3 + 10 + 6 x 25 ) =

= 5⁴⁷ x ( 13 + 150 ) =

= 5⁴⁷ x 163

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c)    13¹⁴ - 13¹³ x 2 - 13¹²  = 13¹² x 142

= 13¹² x ( 13² - 13 x 2 - 1 ) =

= 13¹² x ( 169 - 26 - 1 ) =

= 13¹² x 142