Question

5-Resulva os produtos notáveis:
a)(a + 2b)
b)(3 - 2x)3
d)(x + 5)
c)(2a - 1)3

essa aí!!!​

Answer 1

Resposta:

$(a+2b)^3\\\\\mathrm{Aplique\:a\:formula\:do\:cubo\:perfeito}:\quad \left(a+b\right)^3=a^3+3a^2b+3ab^2+b^3\\\\a=a,\:\:b=2b\\\\=a^3+3a^2\cdot \:2b+3a\left(2b\right)^2+\left(2b\right)^3\\\\=a^3+6a^2b+12ab^2+8b^3\\\\\\\\(3-2x)^3\\\\\mathrm{Aplique\:a\:formula\:do\:cubo\:perfeito}:\quad \left(a-b\right)^3=a^3-3a^2b+3ab^2-b^3\\\\a=3,\:\:b=2x\\\\=3^3-3\cdot \:3^2\cdot \:2x+3\cdot \:3\left(2x\right)^2-\left(2x\right)^3\\\\=27-54x+36x^2-8x^3\\\\=-8x^3+36x^2-54x+27\\\\\\\\(x+5)^3$

$\mathrm{Aplique\:a\:formula\:do\:cubo\:perfeito}:\quad \left(a+b\right)^3=a^3+3a^2b+3ab^2+b^3\\\\a=x,\:\:b=5\\\\=x^3+3x^2\cdot \:5+3x\cdot \:5^2+5^3\\\\=x^3+15x^2+75x+125\\\\\\\\(2a-1)^3\\\\\mathrm{Aplique\:a\:formula\:do\:cubo\:perfeito}:\quad \left(a-b\right)^3=a^3-3a^2b+3ab^2-b^3\\\\a=2a,\:\:b=1\\\\=\left(2a\right)^3-3\left(2a\right)^2\cdot \:1+3\cdot \:2a\cdot \:1^2-1^3\\\\=8a^3-12a^2+6a-1$