Question

Desompuneți in produs utilizând metoda factorului comun.
A) 2^2005 + 2^2003 + 2^2001
B)7^5 + 7^4 + 7^3
C) x^7 + x^6 + x^5
D) 7y^4 + 3y^3 + 2y^2

Dau coroana (hehe)

Answer 1

Răspuns:

Explicație pas cu pas:

A) 2²⁰⁰⁵+2²⁰⁰³+2²⁰⁰¹=2²⁰⁰¹⁺⁴+2²⁰⁰¹⁺²+2²⁰⁰¹=2²⁰⁰¹·2⁴+2²⁰⁰¹·2²+2²⁰⁰¹=

=2²⁰⁰¹·(2⁴+2²+1)=2²⁰⁰¹·(16+4+1)=21·2²⁰⁰¹

B) 7⁵+7⁴+7³=7³·(7²+7¹+1)=7³·(49+7+1)=57·7³

C) x⁷+x⁶+x⁵=x⁵·(x²+x¹+1)

D) 7y⁴+3y³+2y²=y²·(7y²+3y+2)

Answer 2

Răspuns:

Explicație pas cu pas:

a)  2²⁰⁰⁵ + 2²⁰⁰³  + 2²⁰⁰¹ = 2²⁰⁰¹ x 21

= 2²⁰⁰¹ x 2⁴ + 2²⁰⁰¹ x 2² + 2²⁰⁰¹ x 1 =

= 2²⁰⁰¹ x ( 2⁴ + 2² + 1 ) =

= 2²⁰⁰¹ x ( 16 + 4 + 1 ) =

= 2²⁰⁰¹ x 21

_____________________________

b)

7⁵ + 7⁴ + 7³ = 7³ x 57

= 7³ x 7² + 7³ x 7 + 7³ x 1 =

= 7³ x ( 7² + 7 + 1 ) =

= 7³ x ( 49 + 8 ) =

= 7³ x 57

_______________________________________________

c)

x⁷ + x⁶ + x⁵ = x⁵ · ( x² + x + 1 )

= x⁵· x² + x⁵· x + x⁵ · 1 =

= x⁵ · ( x² + x + 1 )

______________________

d)

7 y⁴ + 3 y³ + 2 y² = y² x ( 7 y² + 3 y + 2 )

= y² x 7 y² + y² x 3 y + y² x 2 =

= y² x ( 7 y² + 3 y + 2 )