Question

Me ajudem na resolução dessa questão: Sabendo-se que a= -x/2 e b= -2x,qual é a forma de se escrever a expressão ab^2 - a^3 em função de x?

Answer 1

  ab² - a³
-x/2(-2x)² - (-x/2)³
-x/2(4x²)-(-x³/8)
-4x³/2 + x³/8
-16x³ + x³
       8
-15x³
  8
SE POR ACASO FOR (ab)² - a³, FICA:
(2x²/2)² - (-x/8)
4x⁴/4 + x/8
x⁴ + x/8
8x⁴ + x
    8
  

Answer 2

$ab^{2}-a^{3}=\left(-\dfrac{x}{2}\right)\cdot(-2x)^{2}-\left(-\dfrac{x}{2}\right)^{3}\\\\\\ab^{2}-a^{3}=\left(-\dfrac{x}{2}\right)\cdot(-2)^{2}\cdot x^{2}-\dfrac{(-x)^{3}}{2^{3}}\\\\\\ab^{2}-a^{3}=\left(-\dfrac{x}{2}\right)\cdot4x^{2}-\dfrac{(-x^{3})}{8}\\\\\\ab^{2}-a^{3}=\left(-\dfrac{x}{1}\right)\cdot2x^{2}+\dfrac{x^{3}}{8}\\\\\\ab^{2}-a^{3}=-2x^{3}+\dfrac{x^{3}}{8}\\\\\\ab^{2}-a^{3}=\dfrac{8(-2x^{3})+x^{3}}{8}\\\\\\ab^{2}-a^{3}=\dfrac{-16x^{3}+x^{3}}{8}=-\dfrac{15x^{3}}{8}$

$\boxed{\boxed{ab^{2}-a^{3}=-\dfrac{15x^{3}}{8}}}$