Resposta passo a passo:
a) 3x + 3y =
3.(x + y)
b) 5x² - 10x =
5.x.x - 2.5.x =
5x.(x - 2)
c) x² + 13x =
x.x + 13x =
x.(x + 13)
d) 15x² - 21x =
5.3.x.x - 7.3.x =
3x.(5x - 7)
e) 14x² + 42x =
14.x.x + 3.14.x =
14x.(x + 3)
f ) a² - 12a + 36 =
a² - 2.a.6 + 6² =
(a - 6)²
g) m² - 14m + 49 =
m² - 2.m.7 + 7² =
(m - 7)²
h) a² + 2a + 1 =
a² + 2.a.1 + 1² =
(a + 1)²
i ) x² + 20x + 100 =
x² + 2.x.10 + 10² =
(x + 10)²
j ) 4 + 12x + 9x² =
3²x² + 2.3.x.2 + 2² =
(3x)² + 2.3.x.2 + 2² =
(3x + 2)²
k) 4a² - 25 =
2²a² - 5² =
(2a)² - 5² =
(2a + 5).(2a - 5)
l ) 9a² - 36 =
9.a² - 9.4 =
9.(a² - 4) =
9.(a² - 2²) =
9.(a + 2).(a - 2)
m) 25 - 49x² =
5² - 7²x² =
5² - (7x)² =
(5 + 7x).(5 - 7x)
n ) x² - 121 =
x² - 11² =
(x + 11).(x - 11)
o ) x² - 6x - 16 =
(x² + 2x) + (- 8x - 16) =
(x.x + 2.x) + (- 8.x - 8.2) =
x.(x + 2) + (- 8).(x + 2) =
(x + 2).(x - 8)
p) x² + 10x + 21 =
(x² + 3x) + (7x + 21) =
(x.x + 3.x) + (7x + 3.7) =
x.(x + 3) + 7.(x + 3) =
(x + 3).(x + 7)
