Question

quais sao os produtos notaveis

Answer 1

Quadrado da soma:

 

$(\text{a}+\text{b})^2=(\text{a}+\text{b})\cdot(\text{a}+\text{b})$, com $\text{a}, \text{b}\in\mathbb{R}$.

 

Donde, segue:

 

$(\text{a}+\text{b})^2=\text{a}^2+\text{ab}+\text{ba}+\text{b}^2$

 

$(\text{a}+\text{b})^2=\text{a}^2+2\text{ab}+\text{b}^2$

 

 

Quadrado da diferença:

 

$(\text{a}-\text{b})^2=(\text{a}-\text{b})\cdot(\text{a}-\text{b})$, com $\text{a}, \text{b}\in\mathbb{R}$.

 

Donde, segue:

 

$(\text{a}-\text{b})^2=\text{a}^2-\text{ab}+\text{ba}+\text{b}^2$

 

$(\text{a}-\text{b})^2=\text{a}^2-2\text{ab}+\text{b}^2$

 

 

Produto de uma soma por uma diferença:

 

$(\text{a}+\text{b})\cdot(\text{a}-\text{b})$, com $\text{a}, \text{b}\in\mathbb{R}$.

 

Donde, segue:

 

$(\text{a}+\text{b})\cdot(\text{a}-\text{b})=\text{a}^2-\text{ab}+\text{ab}-\text{b}^2$

 

$(\text{a}+\text{b})\cdot(\text{a}-\text{b})=\text{a}^2-\text{b}^2$

 

 

Cubo de uma soma:

 

$(\text{a}+\text{b})^3=(\text{a}+\text{b})\cdot(\text{a}+\text{b})\cdot(\text{a}+\text{b})$, com $\text{a}, \text{b}\in\mathbb{R}$.

 

Donde, temos:

 

$(\text{a}+\text{b})^3=\text{a}^3+2\text{a}^2\text{b}+\text{ab}^2+\text{a}^2\text{b}+2\text{ab}^2+\text{b}^3$

 

$(\text{a}+\text{b})^3=\text{a}^3+3\text{a}^2\text{b}+3\text{ab}^2+\text{b}^3$

 

 

Cubo de uma diferença:

 

$(\text{a}-\text{b})^3=(\text{a}-\text{b})\cdot(\text{a}-\text{b})\cdot(\text{a}-\text{b})$, com $\text{a}, \text{b}\in\mathbb{R}$.

 

Donde, temos:

 

$(\text{a}-\text{b})^3=\text{a}^3-2\text{a}^2\text{b}+\text{ab}^2-\text{a}^2\text{b}+2\text{ab}^2-\text{b}^3$

 

$(\text{a}-\text{b})^3=\text{a}^3-3\text{a}^2\text{b}+3\text{ab}^2-\text{b}^3$

Answer 2

Só faltou essa:

 

$<var>(x+y+z)^{3}= x^{2} + y^{2} + z^{2} + 2xy + 2xz + 2yz =)</var>$