calculați folosind factorul comun a)2²¹+2¹⁹,b)3²⁴+3²⁵,c(5³⁷-5³⁶,d)2²²-2²¹+2¹⁸,,e)3²⁹-3²⁷+3²⁶;,f)2²⁶+2²⁴+2²⁰
Răspunsuri la întrebare
Răspuns:
a) 2²¹ + 2¹⁹ = (2¹⁹ • 2²) + (2¹⁹ + 2⁰)
= 2¹⁹ • ( 2² + 1)
= 2¹⁹ • (4 + 1 )
= 2¹⁹ • 5
b) 3²⁴ + 3²⁵ = ( 3²⁴ • 3⁰ ) + ( 3²⁴ • 3¹)
= 3²⁴ • ( 1 + 3)
= 3²⁴ • 4
c) 5³⁷ - 5³⁶ = (5³⁶ • 5¹) - ( 5³⁶ • 5⁰)
= 5³⁶ • ( 5¹ - 1)
= 5³⁶ • 4
d) 2²² - 2²¹ + 2¹⁸ = ( 2¹⁸ • 2⁴) - (2¹⁸ • 2³) + (2¹⁸ • 2⁰)
= 2¹⁸ • (2⁴ - 2³ + 2⁰)
= 2¹⁸ • (16 - 8 + 1)
= 2¹⁸ • ( 8+1)
= 2¹⁸ • 9
e) 3²⁹-3²⁷+3²⁶=(3²⁶•3³)-(3²⁶•3¹)+(3²⁶•3⁰)
= 3²⁶•(3³-3¹+1)
=3²⁶•(27-3+1)
=3²⁶•(24+1)
=3²⁶•25
f) 2²⁶+2²⁴+2²⁰=(2²⁰•2⁶)+(2²⁰•2⁴)+(2²⁰•2⁰)
=2²⁰•(2⁶+2⁴+1)
=2²⁰•(64+16+1)
=2²⁰• 81