Question

3. Fatore as expressões algébricas. a) 14a2b + 21ab3 = b) 12ax2 – 4a2x3 = c) 9x2 – 16y2 = d) 64a4 – 100 = e) 9x2 + 12x + 4 = f) 25a2 + 10az + z2 = g) x2 + 4x – 12 = h) x2 – 14x + 40=
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Answer 1

Explicação passo-a-passo:

a)

14a²b + 21ab³ = 7ab.(2a + 3b²)

b)

12ax² - 4a²x³ = 4ax².(3 - ax)

c)

9x² - 16y² = (3x)² - (4y)²

9x² - 16y² = (3x + 4y).(3x - 4y)

d)

64a⁴ - 100 = (8a²)² - 10²

64a⁴ - 100 = (8a² + 10).(8a² - 10)

e)

9x² + 12x + 4 = 9x² + 6x + 6x + 4

9x² + 12x + 4 = 3x.(3x + 2) + 2.(3x + 2)

9x² + 12x + 4 = (3x + 2).(3x + 2)

9x² + 12x + 4 = (3x + 2)²

f)

25a² + 10az + z² = 25a² + 5az + 5az + z²

25a² + 10az + z² = 5a.(5a + z) + z.(5a + z)

25a² + 10az + z² = (5a + z).(5a + z)

25a² + 10az + z² = (5a + z)²

g)

x² + 4x - 12 = x² - 2x + 6x - 12

x² + 4x - 12 = x.(x - 2) + 6.(x - 2)

x² + 4x - 12 = (x - 2).(x + 6)

h)

x² - 14x + 40 = x² - 4x - 10x + 40

x² - 14x + 40 = x.(x - 4) - 10.(x - 4)

x² - 14x + 40 = (x - 4).(x - 10)