Question

Aplique os produtos notáveis. (Socorro!)rs

Answer 1

$a)\ \left(\dfrac{2}{3}bs^3+\dfrac{5}{4}a^2\right)^3\\\\\\ =\left(\dfrac{2^3}{3^3}b^3s^{(3 \times 3)}\right)+3\left(\dfrac{2^2}{3^2}b^2s^{(3 \times 2)} \right)\left( \dfrac{5}{4}a^2\right)\\\\\\ +3\left(\dfrac{2}{3}bs^3\right)\left(\dfrac{5^2}{4^2}a^{(2\times2)}\right)+\left(\dfrac{5^3}{4^3}a^{(2 \times 3)} \right)$

$=\left(\dfrac{8}{27}b^3s^9\right)+\left(\dfrac{3 \times 2^2 \times 5}{3^2 \times 4}b^2s^6a^2\right)+\left(\dfrac{3 \times 2 \times 5^2}{3 \times 4^2}bs^3a^4\right)+\left(\dfrac{125}{64}a^6\right)\\\\\\ =\dfrac{8}{27}b^3s^9+\dfrac{60}{36}b^2s^6a^2+\dfrac{150}{48}bs^3a^4+\dfrac{125}{64}a^6\\\\\\ \boxed{=\dfrac{8}{27}b^3s^9+\dfrac{5}{3}b^2s^6a^2+\dfrac{75}{24}bs^3a^4+\dfrac{125}{64}a^6}$


$b)\ (7xy-6m^3n^2)(7xy+6m^3n^2)\\\\ =7^2s^2y^2-6^2m^{(3\times2)}n^{(2 \times 2)}\\\\ \boxed{=49s^2y^2-36m^6n^4}$


$c)\ \left(x^3+\dfrac{2}{3}y \right)^2\\\\ =x^{(3 \times 2)} + 2(x^3)(\dfrac{2}{3}y)+\dfrac{2^2}{3^2}y^2\\\\ =x^6 + 2.\dfrac{2}{3}x^3y+\dfrac{4}{9}y^2\\\\ \boxed{=x^6 + \dfrac{4}{3}x^3y+\dfrac{4}{9}y^2}$


$d)\ (7y^2+3y^4)^2\\\\ =7^2y^{(2 \times 2)} +2(7y^2)(3y^4)+3^2y^{(4 \times 2)}\\\\ =49y^4 +2.7.3y^{(2+4)}+9y^8\\\\ \boxed{=49y^4 +42y^6+9y^8}$

Bons estudos!