Question

Fatore as expressões:
a) 81x² - 54 a x + 9 a² =
b) 16x – 12y – 4a =
c) 7m a + 7b + y m a + y b=
d) 169a² - 64 b²=

Answer 1

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$\tt{a)}~\sf{81x^2-54ax+9a^2=(9x-3a)^2}\\\tt{b)}~\sf{16x-12y-4a=4\cdot(4x-3y-a)}\\\tt{c)}~\sf{7ma+7b+yma+yb=7ma+yma+7b+yb}\\\sf{ma\cdot(7+y)+b\cdot(7+y)}\\\sf{(7+y)\cdot(ma+b)}\\\tt{d)}~\sf{169a^2-64b^2=(13a-8b)\cdot(13a+8b)}$

Answer 2

Oie, Td Bom?!

a)

$= 81 x{}^{2} - 54ax + 9a {}^{2}$

$= 9(9x {}^{2} - 6ax + a {}^{2} )$

$= 9(3 {}^{2} x {}^{2} - 2 \: . \: 3x \: . \: a + a {}^{2} )$

$= 9((3x) {}^{2} - 2 \: . \: 3x \: . \: a + a {}^{2} )$

$= 9(3x - a) {}^{2}$

b)

$= 16x - 12y - 4a$

$= 4(4x - 3y - a)$

c)

$= 7ma + 7b + yma + yb$

$= 7(ma + b) + y \: . \: (ma + b)$

$= (ma + b) \: . \: (7 + y)$

$= (am + b) \: . \: (7 + y)$

d)

$= 169a {}^{2} - 64b {}^{2}$

$= 13 {}^{2} a {}^{2} - 8 {}^{2} b {}^{2}$

$= (13a) {}^{2} - (8b) {}^{2}$

$= (13a - 8b) \: . \: (13a + 8b)$

Att. Makaveli1996