# 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 1Set 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 2Set 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 3Set 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 = -0.25bSolutiona = {b, -0.25b}`