Question

5y(y2-2a)+a(2y-a2)=5y3+a(8y+a2)

Answer 1

$5y*(y^2-2a)+a*(2y-a^2)=5y^3+a*(8y+a^2);$

$5y^3-10ay+2ay-a^3=5y^3+8ay+a^3;$

$2a^3+16ay=0; a^3+8ay=0.$

Дальнейшее решение зависит от того, относительно какой переменной решать уравнение.

Если относительно y (что более вероятно), то:

$a^2+8y=0; y=\frac{-a^2}{8}$

Если относительно a, то:

$a(a^2+8y)=0;$ a=0 или $a^2+8y=0; a={\pm\sqrt{-8y}}, { }y{\leq}0$

Answer 2

To solve the equation 5y(y^2 - 2a) + a(2y - a^2) = 5y^3 + a(8y + a^2), you can start by simplifying and rearranging the terms on both sides of the equation to isolate the variable y:

1. Expand the terms on both sides of the equation:

   5y(y^2) - 5y(2a) + a(2y) - a(a^2) = 5y^3 + 8ay + a^3

2. Now, distribute the constants and simplify:

   5y^3 - 10ay + 2ay - a^3 = 5y^3 + 8ay + a^3

3. Combine like terms on both sides of the equation:

   5y^3 - 8ay - 10ay + 2ay - a^3 = 5y^3 + 8ay + a^3

4. Group like terms:

   5y^3 - (8ay + 10ay - 2ay) - a^3 = 5y^3 + 8ay + a^3

5. Combine the terms with 'ay':

   5y^3 - 16ay - a^3 = 5y^3 + 8ay + a^3

6. Now, subtract 5y^3 from both sides of the equation to get the variable terms on one side:

   -16ay - a^3 = 8ay + a^3

7. Add 16ay to both sides to isolate the 'a' terms:

   -a^3 = 8ay + a^3 + 16ay

8. Combine 'a' terms on the right side:

   -a^3 = 24ay + a^3

9. Add a^3 to both sides:

   0 = 24ay + 2a^3

10. Now, divide both sides by 2a to solve for 'y':

0 = 12y + a^2

11. Subtract a^2 from both sides:

-a^2 = 12y

12. Finally, divide both sides by -a^2:

y = -12/a^2

So, the solution to the equation is y = -12/a^2.