Question

Resolva os produtos notáveis seguintes:

a) (a+5)³
b) (b+3)³
c) (t+2)³
d) (k+1)³
e) (p-7)³
f) (q-3)³

Answer 1

Explicação passo-a-passo:

Cubo da soma

(a+b)³=a³+3a²b+3b²a+b³

a) (a+5)³=>a³+15a²+75a+125

b) (b+3)³=>b³+9b²+27b+27

c) (t+2)³=>t³+6t²+12t+8

d) (k+1)³=>k³+3k²+3k+1

Cubo da diferença

(a-b)³=a³-3a²b+3b²a-b³

e) (p-7)³=>p³-21p²+147p-343

f) (q-3)³=>q³-9q²+27q-27

Answer 2

Oie, Td Bom?!

a)

$= (a + 5) {}^{3}$

$= a {}^{3} + 3a {}^{2} \: . \: 5 + 3a \: . \: 5 {}^{2} + 5 {}^{3}$

$= a {}^{3} + 15a {}^{2} + 75a + 125$

b)

$= (b + 3) {}^{3}$

$= b {}^{3} + 3b {}^{2} \: . \: 3 + 3b \: . \: 3 {}^{2} + 3 {}^{3}$

$= b {}^{ 3} + 9b {}^{2} + 27b + 27$

c)

$= (t + 2) {}^{3}$

$= t {}^{3} + 3t {}^{2} \: . \: 2 + 3t \: . \: 2 {}^{2} + 2 {}^{3}$

$= t {}^{3} + 6t {}^{2} + 12t + 8$

d)

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

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

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

e)

$= (p - 7) {}^{3}$

$= p {}^{3} - 3p {}^{2} \: . \: 7 + 3p \: . \: 7 {}^{2} - 7 {}^{3}$

$= p {}^{3} - 21p {}^{2} + 147p - 343$

f)

$= (q - 3) {}^{3}$

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

$= q {}^{3} - 9q {}^{2} + 27q - 27$

Att. Makaveli1996