Question

ATIVIDADE 08 - Resolva:
a) (a + b) ³
b) (b-c)³
c) (2x + y)³
d) (3y - 1)³​

Answer 1

Resposta:

Explicação passo a passo:

ATIVIDADE 08 - Resolva:

a) (a + b) ³

$(a + b)^3=\\\mathrm{Aplique\:a\:formula\:do\:cubo\:perfeito\:e\:ficara:}\:\\\\quad \left(a+b\right)^3=a^3+3a^2b+3ab^2+b^3$

b) (b-c)³

$\mathrm{Aplique\:a\:formula\:do\:cubo\:perfeito}:\quad \left(a-b\right)^3=a^3-3a^2b+3ab^2-b^3\\\\\left(b-c\right)^3=b^3-3b^2c+3bc^2-c^3$

c) (2x + y)³

$\mathrm{Aplique\:a\:formula\:do\:cubo\:perfeito}:\quad \left(a+b\right)^3=a^3+3a^2b+3ab^2+b^3\\\\\left(2x+y\right)^3=\left(2x\right)^3+3\left(2x\right)^2y+3\cdot \:2xy^2+y^3\\(2x+y)^3=8x^3+12x^2y+6xy^2+y^3$

d) (3y - 1)³​

$\mathrm{Aplique\:a\:formula\:do\:cubo\:perfeito}:\quad \left(a-b\right)^3=a^3-3a^2b+3ab^2-b^3\\\\\left(3y-1\right)^3=\left(3y\right)^3-3\left(3y\right)^2\cdot \:1+3\cdot \:3y\cdot \:1^2-1^3\\(3y-1)^3=27y^3-27y^2+9y-1$