Question

Fatore as expressões.

a) am+na+bm+bn=
b) xy-yz+wx-wz=
c) ax+bx+ay+by=
d) 5ab+ac+5bd+cd=
e) 7x+7y+ax+ay=

Answer 1

$am+na+bm+bn= \\ a(m + n) +b (m + n) = \\ (a + b)(m + n)$

$xy-yz+wx-wz= \\ y(x - z) + w(x - z) = \\ (y + w)(x - z)$

$ax+bx+ay+by= \\ x(a + b) + y(a + b) = \\ (x + y)(a + b)$

$5ab+ac+5bd+cd= \\ a(5b + c) + d(5b + c) = \\ (a + d)(5b + c)$

$7x+7y+ax+ay= \\ 7(x + y) + a(x + y) = \\ (7 + a)(x + y)$

Answer 2

Resposta:

a)

$am + na + bm +b n \\ \\ a( m+ n) + b(m + n) \\ \\ \Large\boxed{ \green{ (m + n)(a + b)}}$

b)

$xy - yz + wx - wz \\ \\ y(x - z) + w(x - z) \\ \\ \Large\boxed{ \green{ (x - z)(y + w)}}$

c)

$ax + bx + ay + by \\ \\ x(a + b) + y(a + b) \\ \\ \Large \boxed{ \green{(a + b)(x + y)}}$

d)

$5ab + ac + 5bd + cd \\ \\ a(5b + c) + d(5b + c) \\ \\ \Large \boxed{ \green{(5b + c)(a + d)}}$

e)

$7x + 7y + ax + ay \\ \\ 7(x + y) + a(x + y) \\ \\ \Large \boxed{ \green{(x + y)(7 + a)}} \\ \\ \Large\boxed{ \underline{ \blue{ \bf \: Bons \: Estudos!}}}$