b^8-p^8=0

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Solution for b^8-p^8=0 equation:


Simplifying
b8 + -1p8 = 0

Solving
b8 + -1p8 = 0

Solving for variable 'b'.

Move all terms containing b to the left, all other terms to the right.

Add 'p8' to each side of the equation.
b8 + -1p8 + p8 = 0 + p8

Combine like terms: -1p8 + p8 = 0
b8 + 0 = 0 + p8
b8 = 0 + p8
Remove the zero:
b8 = p8

Simplifying
b8 = p8

Combine like terms: p8 + -1p8 = 0
b8 + -1p8 = 0

Factor a difference between two squares.
(b4 + p4)(b4 + -1p4) = 0

Factor a difference between two squares.
(b4 + p4)((b2 + p2)(b2 + -1p2)) = 0

Factor a difference between two squares.
(b4 + p4)((b2 + p2)((b + p)(b + -1p))) = 0

Subproblem 1

Set the factor '(b4 + p4)' equal to zero and attempt to solve: Simplifying b4 + p4 = 0 Solving b4 + p4 = 0 Move all terms containing b to the left, all other terms to the right. Add '-1p4' to each side of the equation. b4 + p4 + -1p4 = 0 + -1p4 Combine like terms: p4 + -1p4 = 0 b4 + 0 = 0 + -1p4 b4 = 0 + -1p4 Remove the zero: b4 = -1p4 Simplifying b4 = -1p4 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 '(b2 + p2)' equal to zero and attempt to solve: Simplifying b2 + p2 = 0 Solving b2 + p2 = 0 Move all terms containing b to the left, all other terms to the right. Add '-1p2' to each side of the equation. b2 + p2 + -1p2 = 0 + -1p2 Combine like terms: p2 + -1p2 = 0 b2 + 0 = 0 + -1p2 b2 = 0 + -1p2 Remove the zero: b2 = -1p2 Simplifying b2 = -1p2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 3

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

Subproblem 4

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

Solution

b = {-1p, p}

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