Question

desenvolva os Produtos a seguir: 
a) (x+3/2)³=
b) (3x-1/7)³=

Answer 1

Temos que:

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

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

Assim:

a) $(x+\frac{3}{2})^3=x^3+3\cdot x^2\cdot\left(\frac{3}{2}\right)+3\cdot x\cdot\left(\frac{3}{2}\right)^2+\left(\frac{3}{2}\right)^3$

$(x+\frac{3}{2})^3=x^3+\dfrac{9x^2}{2}+\frac{27x}{4}+\frac{27}{8}$

b) $(3x-\frac{1}{7})=(3x)^3-3\cdot(3x)^2\cdot\left(\frac{1}{7}\right)+3\cdot3x\cdot\left(\frac{1}{7}\right)^2-\left(\frac{1}{7}\right)^3$

$(3x-\frac{1}{7})=27x^3-\frac{27x^2}{7}+\frac{9x}{49}-\frac{1}{343}$.