4a^2b^3+ab^4-4ab^4-b^5=

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Solution for 4a^2b^3+ab^4-4ab^4-b^5= equation:


Simplifying
4a2b3 + ab4 + -4ab4 + -1b5 = 0

Reorder the terms:
ab4 + -4ab4 + 4a2b3 + -1b5 = 0

Combine like terms: ab4 + -4ab4 = -3ab4
-3ab4 + 4a2b3 + -1b5 = 0

Solving
-3ab4 + 4a2b3 + -1b5 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'b3'.
b3(-3ab + 4a2 + -1b2) = 0

Factor a trinomial.
b3((a + -1b)(4a + b)) = 0

Subproblem 1

Set the factor 'b3' equal to zero and attempt to solve: Simplifying b3 = 0 Solving b3 = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b3' to each side of the equation. b3 + -1b3 = 0 + -1b3 Remove the zero: 0 = -1b3 Simplifying 0 = -1b3 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(a + -1b)' equal to zero and attempt to solve: Simplifying a + -1b = 0 Solving a + -1b = 0 Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. a + -1b + b = 0 + b Combine like terms: -1b + b = 0 a + 0 = 0 + b a = 0 + b Remove the zero: a = b Simplifying a = b

Subproblem 3

Set the factor '(4a + b)' equal to zero and attempt to solve: Simplifying 4a + b = 0 Solving 4a + b = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. 4a + b + -1b = 0 + -1b Combine like terms: b + -1b = 0 4a + 0 = 0 + -1b 4a = 0 + -1b Remove the zero: 4a = -1b Divide each side by '4'. a = -0.25b Simplifying a = -0.25b

Solution

a = {b, -0.25b}

 

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