Question

2 - Qual é o desenvolvimento do binômio:
(2x - 1)⁴
a) 16x⁵ - 32³ + 24x² - 8x - 1
b) 16x⁴ - 32² + 24x³ + 8x - 1
c) 16x⁵ 32³ + 24x² - 8x + 1
d) 16x⁴ - 32³+24x² - 8x + 1​

Answer 1

Oie, Td Bom?!

$= (2x - 1) {}^{4}$

$= (2x - 1) {}^{2 + 2}$

$= (2x - 1) {}^{2} \: . \: (2x -1 ) {}^{2}$

$= ((2x) {}^{2} - 2 \: . \: 2x \: . \: 1 + 1 {}^{2} ) \: . \: ((2x) {}^{2} - 2 \: . \: 2x \: . \: 1 + 1 {}^{2} )$

$= (4x {}^{2} - 4x + 1) \: . \: (4x {}^{2} - 4x + 1)$

$= 4x {}^{2} \: . \: (4x {}^{2} - 4x + 1) - 4x \: . \: (4x {}^{2} - 4x + 1) + 1(4x {}^{2} - 4x + 1)$

$= 16x {}^{4} - 16x {}^{3} + 4x {}^{2} - 16x {}^{3} + 16x {}^{2} - 4x + 4x {}^{2} - 4x + 1$

$= 16x {}^{4} - 32x {}^{3} + 24x {}^{2} - 8x + 1$

Att. Makaveli1996