Question

1 Resolva as expressões abaixo:
a) (p + q)³

b) (x + 1)³

c) (x + 2y)³

d) (x – 2)³

e) (2x – 1)³

Answer 1

Oie, Td Bom?!

■ Cubo da soma de 2 termos:

$(a + b) {}^{3} = a {}^{3} + 3a {}^{2} b + 3ab {}^{2} + b {}^{3}$

■ Cubo da diferença de 2 termos:

$(a - b) {}^{3} = a {}^{3} - 3a {}^{2} b + 3ab {}^{2} - b {}^{3}$

a)

$= (p + q) {}^{3}$

$= p {}^{3} + 3p {}^{2} q + 3pq {}^{2} + p {}^{3}$

b)

$= (x + 1) {}^{3}$

$= x {}^{3} + 3x {}^{2} \: . \: 1 + 3x \: . \: 1 {}^{2} + 1 {}^{3}$

$= x {}^{3} + 3x {}^{2} + 3x + 1$

c)

$= (x + 2y) {}^{3}$

$= x {}^{3} + 3x {}^{2} \: . \: 2y + 3x \: . \: (2y) {}^{2} + (2y) {}^{3}$

$= x {}^{3} + 6x {}^{2} y + 12xy {}^{2} + 8y {}^{3}$

d)

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

$= x {}^{3} - 3x {}^{2} \: . \: 2 + 3x \: . \: 2 {}^{2} - 2 {}^{3}$

$= x {}^{3} - 6x {}^{2} + 12x - 8$

e)

$= (2x - 1) {}^{3}$

$= (2x) {}^{3} - 3 \: . \: (2x) {}^{2} \: . \: 1 + 3 \: . \: 2x \: . \: 1 {}^{2} - 1 {}^{3}$

$= 8x {}^{3} - 12x {}^{2} + 6x - 1$

Att. Makaveli1996

Answer 2

Explicação passo-a-passo:

a)

(p + q)³ = p³ + 3.p².q + 3.p.q² + q³

(p + q)³ = p³ + 3p²q + 3pq² + q³

b)

(x + 1)³ = x³ + 3.x².1 + 3.x.1² + 1³

(x + 1)³ = x³ + 3x² + 3x + 1

c)

(x + 2y)³ = x³ + 3.x².2y + 3.x.(2y)² + (2y)³

(x + 2y)³ = x³ + 6x²y + 3.x.4y² + 8y³

(x + 2y)³ = x³ + 6x²y + 12xy² + 8y³

d)

(x - 2)³ = x³ - 3.x².2 + 3.x.2² - 2³

(x - 2)³ = x³ - 6x² + 3.x.4 - 8

(x - 2)³ = x³ - 6x² + 12x - 8

e)

(2x - 1)³ = (2x)³ - 3.(2x)².1 + 3.2x.1² - 1³

(2x - 1)³ = 8x³ - 3.4x².1 + 3.2x.1 - 1

(2x - 1)³ = 8x³ - 12x² + 6x - 1