1) Fatore as expressões:

a) x³ + 1³
b) x³ - 1³
c) x³ + 8
d) x³ - 8
e) 1000x³ + 125y³
f) 1000x³ - 125y³

Q: 1) Fatore as expressões: a) x³ + 1³ b) x³ - 1³ c) x³ + 8 d) x³ - 8 e) 1000x³ + 125y³ f) 1000x³ - 125y³

Vamos fatorar as expressões: a) $x^3 + 1^3$ \[ x^3 + 1 = (x + 1)(x^2 - x + 1) \] b) $x^3 - 1^3$ \[ x^3 - 1 = (x - 1)(x^2 + x + 1) \] c) $x^3 + 8$ \[ x^3 + 8 = (x + 2)(x^2 - 2x + 4) \] d) $x^3 - 8$ \[ x^3 - 8 = (x - 2)(x^2 + 2x + 4) \] e) $1000x^3 + 125y^3$ \[ 1000x^3 + 125y^3 = (10x + 5y)(100x^2 - 50xy + 25y^2) \] f) $1000x^3 - 125y^3$ \[ 1000x^3 - 125y^3 = (10x - 5y)(100x^2 + 50xy + 25y^2) \]

Question

1) Fatore as expressões:

a) x³ + 1³
b) x³ - 1³
c) x³ + 8
d) x³ - 8
e) 1000x³ + 125y³
f) 1000x³ - 125y³

Accepted Answer

Vamos fatorar as expressões:

a) $x^3 + 1^3$

$$ 
x^3 + 1 = (x + 1)(x^2 - x + 1) 
$$

b) $x^3 - 1^3$

$$ 
x^3 - 1 = (x - 1)(x^2 + x + 1) 
$$

c) $x^3 + 8$

$$ 
x^3 + 8 = (x + 2)(x^2 - 2x + 4) 
$$

d) $x^3 - 8$

$$ 
x^3 - 8 = (x - 2)(x^2 + 2x + 4) 
$$

e) $1000x^3 + 125y^3$

$$ 
1000x^3 + 125y^3 = (10x + 5y)(100x^2 - 50xy + 25y^2) 
$$

f) $1000x^3 - 125y^3$

$$ 
1000x^3 - 125y^3 = (10x - 5y)(100x^2 + 50xy + 25y^2) 
$$

1) Fatore as expressões: a) x³ + 1³ b) x³ - 1³ c) x³ + 8 d)...

Fatore as expressões:

a) x³ + 1³ b) x³ - 1³ c) x³ + 8 d) x³ - 8 e) 1000x³ + 125y³ f) 1000x³ - 125y³

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