Question

ajutor va rog!!! multumesc

Answer 1

Răspuns:

Explicație pas cu pas:

a) (2x+5)⁴=C₄⁰·(2x)⁴+C₄¹·(2x)³·5+C₄²·(2x)²·5²+C₄³·(2x)·5³+C₄⁴·5⁴=

(4!/4!·0!)·(2x)⁴+(4!/3!·1!)·(2x)³·5+(4!/2!·2!)·(2x)²·5²+(4!/1!·3!)·(2x)·5³+

(4!/0!·4!)·5⁴=1·(2x)⁴+4·(2x)³·5+6·(2x)²·5²+4·(2x)·5³+1·5⁴=

16x⁴+160x³+600x²+1000x+625

C₄⁰=4!/(4-0)!0!=1·2·3·4/1·2·3·4·1=1

C₄¹=4!/(4-1)!·1!=1·2·3·4/1·2·3·1=4

C₄²=4!/(4-2)!·2!=1·2·3·4/1·2·1·2=3·2=6

C₄³=4!/(4-3)!·3!=1·2·3·4/1·1·2·3=4

C₄⁴=4!/0!·4!=1·2·3·4/1·1·2·3·4=1

b) (x+5)⁵=C₅⁰·x⁵+C₅¹·x⁴·5+C₅²·x³·5²+C₅³·x²·5³+C₅⁴·x·5⁴+C₅⁵·5⁵=

(5!/5!·0!)·x⁵+(5!/4!·1!)·x⁴·5+(5!/3!·2!)·x³·5²+(5!/2!·3!)·x²·5³+(5!/1!·4!)·x·5⁴+      (5!/0!·5!)·5⁵=1·x⁵+5·x⁴·5+10·x³·5²+10·x²·5³+5·x·5⁴+1·5⁵=

x⁵+25x⁴+250x³+1250x²+3125x+3125        

C₅⁰=5!/5!·0!=1·2·3·4·5/1·2·3·4·5·1=1

C₅¹=5!/4!·1!=1·2·3·4·5/1·2·3·4·1=5

C₅²=5!/3!·2!=1·2·3·4·5/1·2·3·1·2=10

C₅³=5!/2!·3!=1·2·3·4·5/1·2·1·2·3=10

C₅⁴=5!/1!·4!=1·2·3·4·5/1·1·2·3·4=5

C₅⁵=5!/0!·5!=1·2·3·4·5/1·1·2·3·4·5=1