Question

Resolva os produtos abaixo até a forma irredutível
a. ( x+9)² = (x+9) • (x+9) =

b. (3-a)² =

c. (x+7) • (x-7) =

d. (x+2y) • (z-×y) =

e. (3y²-2)² =

f. ( 5-m³)² =

me ajudem pf, urgente ​

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{(x + 9)^2 = (x + 9).(x + 9)}$

$\mathsf{(x + 9)^2 = x^2 + 9x + 9x + 81}$

$\mathsf{(x + 9)^2 = x^2 + 18x + 81}$

$\mathsf{(3 - a)^2 = (3 - a).(3 - a)}$

$\mathsf{(3 - a)^2 = 9 - 3a - 3a + a^2}$

$\mathsf{(3 - a)^2 = 9 - 6a + a^2}$

$\mathsf{(x + 7).(x - 7) = x^2 - 7x + 7x - 49}$

$\mathsf{(x + 7).(x - 7) = x^2 - 49}$

$\mathsf{(x + 2y).(z - xy) = xz - x^2y+ 2yz - 2xy^2}$

$\mathsf{(3y^2 - 2)^2 = (3y^2 - 2).(3y^2 - 2)}$

$\mathsf{(3y^2 - 2)^2 = 9y^4 - 6y^2 - 6y^2 + 4}$

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

$\mathsf{(5 - m^3)^2 = (5 - m^3).(5 - m^3)}$

$\mathsf{(5 - m^3)^2 = 25 - 5m^3 - 5m^3 + m^6}$

$\mathsf{(5 - m^3)^2 = 25 - 10m^3 + m^6}$

Answer 2

✅ Desenvolvendo os produtos notáveis:

• A)

         $\Large\displaystyle\begin{gathered} (x + 9)^{2} = (x + 9)\cdot(x + 9)\end{gathered}$

                            $\Large\displaystyle\begin{gathered} = x\cdot x + x\cdot 9 + 9\cdot x + 9\cdot9\end{gathered}$

                            $\Large\displaystyle\begin{gathered} = x^{2} + 9x + 9x + 81\end{gathered}$

                            $\Large\displaystyle\begin{gathered} = x^{2} + 18x + 81\end{gathered}$

• B)

         $\Large\displaystyle\begin{gathered} (3 - a)^{2} = (3 - a)\cdot(3 - a)\end{gathered}$

                            $\Large\displaystyle\begin{gathered} = 3\cdot3 - 3\cdot a - a\cdot3 + a\cdot a\end{gathered}$

                            $\Large\displaystyle\begin{gathered} = 9 - 3a - 3a + a^{2}\end{gathered}$

                            $\Large\displaystyle\begin{gathered} = 9 -6a + a^{2}\end{gathered}$

• C)

         $\Large\displaystyle\begin{gathered} (x + 7)\cdot(x - 7) = x\cdot x - x\cdot 7 + 7\cdot x - 7\cdot 7\end{gathered}$

                                             $\Large\displaystyle\begin{gathered} = x^{2} - 7x + 7x - 49\end{gathered}$

                                             $\Large\displaystyle\begin{gathered} = x^{2} - 49\end{gathered}$

• D)

        $\Large\displaystyle\begin{gathered} (x + 2y)\cdot(z - xy) = x\cdot z - x\cdot xy + 2y\cdot z - 2y\cdot xy\end{gathered}$

                                                 $\Large\displaystyle\begin{gathered} = xz - x^{2}y + 2yz - 2xy^{2}\end{gathered}$

                                                 $\Large\displaystyle\begin{gathered} = x(z - xy) + 2y(z - xy)\end{gathered}$

• E)

         $\Large\displaystyle\begin{gathered} (3y^{2} - 2)^{2} = (3y^{2} - 2)\cdot(3y^{2} - 2)\end{gathered}$

                                $\Large\displaystyle\begin{gathered} = 3y^{2}\cdot3y^{2} - 3y^{2}\cdot2 - 2\cdot3y^{2} + 2\cdot2\end{gathered}$

                                $\Large\displaystyle\begin{gathered} = 9y^{4} - 6y^{2} - 6y^{2} + 4\end{gathered}$

                                $\Large\displaystyle\begin{gathered} = 9y^{4} - 12y^{2} + 4\end{gathered}$

• F)

           $\Large\displaystyle\begin{gathered} (5 - m^{3})^{2} = (5 - m^{3})\cdot(5 - m^{3})\end{gathered}$

                                  $\Large\displaystyle\begin{gathered} = 5\cdot5 - 5\cdot m^{3} - m^{3}\cdot5 + m^{3}\cdot m^{3}\end{gathered}$

                                  $\Large\displaystyle\begin{gathered} = 25 - 5m^{3} - 5m^{3} + m^{6}\end{gathered}$

                                  $\Large\displaystyle\begin{gathered} = 25 - 10m^{3} + m^{6}\end{gathered}$

$\LARGE\displaystyle\text{ \begin{gathered} \underline{\boxed{\boldsymbol{\:\:\:Bons \:estudos!!\:\:\:Boa\: sorte!!\:\:\:}}}\end{gathered} }$

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