Question

A) (X+a)5=


B) (X-a)6=


C) (X-2a)5=

Answer 1

Vamos lá:

a)
$\binom{5}{0} {x}^{5} {a}^{0} + \binom{5}{1} {x}^{4} {a}^{1} + \binom{5}{2} {x}^{3} {a}^{2} + \binom{5}{3} {x}^{2} {a}^{3} + \binom{5}{4} {x}^{1} {a}^{4} + \binom{5}{5} {x}^{0} {a}^{5} \\ {x}^{5} + 5 {x}^{4}a + 10 {x}^{3} {a}^{2} + 10 {x}^{2} {a}^{3} + 5x {a}^{4} + {a}^{5}$
b)
$\binom{6}{0} {x}^{6} {a}^{0} - \binom{6}{1} {x}^{5} {a}^{1} + \binom{6}{2} {x}^{4} {a}^{2} - \binom{6}{3} {x}^{3} {a}^{3} + \binom{6}{4} {x}^{2} {a}^{4} - \binom{6}{5} {x}^{1} {a}^{5} + \binom{6}{6} {x}^{0} {a}^{6} \\ {x}^{6} - 6 {x}^{5}a + 15 {x}^{4} {a}^{2} - 20 {x}^{3} {a}^{3} + 15 {x}^{2} {a}^{4} - 6x {a}^{5} + {a}^{6}$
c)
$\binom{5}{0} {x}^{5} {(2a)}^{0} - \binom{5}{1} {x}^{4} {(2a)}^{1} + \binom{5}{2} {x}^{3} {(2a)}^{2} - \binom{5}{3} {x}^{2} {(2a)}^{3} + \binom{5}{4} {x}^{1} {(2a)}^{4} - \binom{5}{5} {x}^{0} {(2a)}^{5} \\ {x}^{5} - 10 {x}^{4}a + 40 {x}^{3} {a}^{2} - 80 {x}^{2} {a}^{3} + 80x {a}^{4} - 32 {a}^{5}$
Espero ter ajudado.