Question

Fatore:

a) 6x² + 12xy + 6y²
b) 4x² - 16y²
c) 3x + 3y + 6x² - 6y²

Answer 1

Oie, Td Bom?!

a)

$= 6x {}^{2} + 12xy + 6y {}^{2}$

$= 6(x {}^{2} + 2xy + y {}^{2} )$

$= 6(x + y) {}^{2}$

b)

$= 4x {}^{2} - 16y {}^{2}$

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

$= 4 \: . \: x {}^{2} - 2 {}^{2} y {}^{2}$

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

$= 4(x - 2y) \: . \: (x + 2y)$

c)

$= 3x + 3y + 6x {}^{2} - 6y {}^{2}$

$= 3(x + y + 2x {}^{2} - 2y {}^{2} )$

$= 3(x + y + 2(x {}^{2} - y {}^{2} ))$

$= 3(x + y + 2(x - y) \: . \: (x + y))$

$= 3(x + y) \: . \: (1 + 2(x - y))$

$= 3(x + y) \: . \: (1 + 2x - 2y)$

Att. Makaveli1996