Question

Desenvolva os produtos notaveis:

(2+x)³

(y+3)³

(2+1,5)³

(5-y)³

(x-2/3)³

(2x+3/2)²

(3y-2)²

Answer 1

a) $(2+\text{x})^3=2^3+3\cdot2^2\cdot\text{x}+3\cdot2\cdot\text{x}^2+\text{x}^3$

 

$(2+\text{x})^3=8+18\text{x}+6\text{x}^2+\text{x}^3$

 

 

b) $(\text{y}+3)^3=\text{y}^3+3\cdot\text{y}^2\cdot3+3\cdot\text{y}\cdot3^2+3^3$

 

$(\text{y}+3)^3=\text{y}^3+9\text{y}^2+27\text{y}+27$

 

 

c) $(2+1,5)^3=2^3+3\cdot2^2\cdot1,5+3\cdot2\cdot(1,5)^2+(1,5)^3$

 

$(2+1,5)^3=8+9+13,5+3,375=33,875$

 

 

d) $(5-\text{y})^3=5^3-3\cdot5^2\cdot\text{y}+3\cdot5\cdot\text{y}^2-\text{y}^3$

 

$(5-\text{y})^3=125-75\text{y}+15\text{y}^2-\text{y}^3$

 

 

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

 

$(\text{x}-\frac{2}{3})~3\text{x}^3-2\text{x}^2+\frac{4}{3}\text{x}+\frac{8}{27}$

 

 

f) $(2\text{x}+\frac{3}{2})^2=(2\text{x})^2+2\cdot2\text{x}\cdot\frac{3}{2}+\left(\frac{3}{2}\right)^2$

 

 

$(2\text{x}+\frac{3}{2})^2=4\text{x}^2+6\text{x}+\frac{9}{4}$

 

 

g) $(3\text{y}-2)^2=(3\text{y})^2-2\cdot3\text{y}\cdot2+2^2$

 

$(3\text{y}-2)^2=9\text{y}^2-12\text{y}+4$

Answer 2

Veja a solução no anexo!!!!  espero que goste!!!