Question

Fatorar as expressões:
a) 9x² - 16y²

b) a² - 9

c) 25 - m⁴

d) a²b⁴ - 1

e) 36x⁴y⁶ - 16a⁴

f) 25m⁴ - 49x⁶y²

Answer 1

a) 
9x² = (3x)²
16y² = (4y)²
---> (3x)² - (4y)² = (3x + 4y).(3x - 4y)

b)
9 = 3²
---> a² - 3² = (a + 3).(a - 3)

c)
25 = 5²
m⁴ = (m²)²
---> 5² - (m²)² = (5 + m²).(5 - m²)

d)
a²b⁴ = (ab²)²
---> (ab²)² - 1 = (ab² + 1).(ab² - 1)

e)
36x⁴y⁶ = (6x²y³)²
16a⁴ = (4a²)²
---> (6x²y³)² - (4a²)² = (6x²y³ + 4a²).(6x²y³ - 4a²)

f)
25m⁴ = (5m²)² 
49x⁶y² = (7x³y)²
---> (5m²)² - (7x³y)² = (5m² + 7x³y).(5m² - 7x³y)