Question

Complete:

a) x² + 12x + 36 = (x+_)²

b) 9x² - 30x + 25 = (_-5)²

c) y² + 2y + 1 = (_+_)²

d) 16a² - 24ab + 9b² = (_-3b)²

Answer 1

Complete:

a) x² + 12x + 36 = (x+_)²
ATENÇÃO
x² = x.x
12x = 6x + 6x
36 = 6.6

assim
x² +12x + 36 = (x + 6)(x + 6) = (x + 6)²


b) 9x² - 30x + 25 = (_-5)²

9x² = 3x.3x
- 30x =  -15x - 15x
25 = (-5)(-5)

assim
x² - 30x + 25 = (3x - 5)(3x - 5) = (3x - 5)²
  

c) y² + 2y + 1 = (_+_)²
y² = y.y
2y = 1y + 1y
1 = 1.1

assim
y² + 2y + 1 = (y + 1)(y + 1) = (y + 1)²

d) 16a² - 24ab + 9b² = (_-3b)²

16a² = 4a .4a
- 24ab = - 12ab - 12ab
9b² = 3b.3b

assim
16a² - 24ab + 9b² = (4a - 3b)(4a - 3b) = (4a - 3b)²