Question

4- Fatore a diferença de dois quadrados: a) a2 – 4= b) 1 – x4 = c) 9 – y6 = d) X4 -100 = e) 16 – 4v8 =

Answer 1

Oie, Td Bom?!

a)

$= a {}^{2} - 4$

$= a {}^{2} - 2 {}^{2}$

$= (a - 2) \: . \: (a + 2)$

b)

$= 1 - x {}^{4}$

$= 1 {}^{2} - x {}^{2 \: .2}$

$= 1 {}^{2} - (x {}^{2} ) {}^{2}$

$= (1 - x {}^{2} ) \: . \: (1 + x {}^{2} )$

c)

$= 9 - y {}^{6}$

$= 3 {}^{2} - y {}^{2 \: . \: 3}$

$= 3 {}^{2} - (y {}^{3} ) {}^{2}$

$= (3 - y {}^{3} ) \: . \: (3 + y {}^{3} )$

d)

$= x {}^{4} - 100$

$= x {}^{2 \: . \: 2} - 10 {}^{2}$

$= (x {}^{2} ) {}^{2} - 10 {}^{2}$

$= (x {}^{2} - 10) \: . \: (x {}^{2} + 10)$

e)

$= 16 - 4v {}^{8}$

$=4(4 - v {}^{8} )$

$= 4(2 {}^{2} - v {}^{2 \: . \: 4} )$

$= 4(2 {}^{2} - (v {}^{4} ) {}^{2} )$

$= 4(2 - v {}^{4} ) \: . \: (2 + v {}^{4} )$

Att. Makaveli1996

Answer 2

Explicação passo-a-passo:

a)

a² - 4 = a² - 2²

a² - 4 = (a + 2).(a - 2)

b)

1 - x⁴ = 1 - (x²)²

1 - x⁴ = (1 + x²).(1 - x²)

1 - x⁴ = (1 + x²).(1 + x).(1 - x)

c)

9 - y⁶ = 3² - (y³)²

9 - y⁶ = (3 + y³).(3 - y³)

d)

x⁴ - 100 = (x²)² - 10²

x⁴ - 100 = (x² + 10).(x² - 10)

e)

16 - v⁸ = 4² - (v⁴)²

16 - v⁸ = (4 + v⁴).(4 - v⁴)

16 - v⁸ = (4 + v⁴).[2² - (v²)²]

16 - v⁸ = (4 + v⁴).(2 + v²).(2 - v²)