What are the solutions to the equation solvefor a,a^2b-b^3=(2ab-2b^2) ?

The solutions to the equation solvefor a,a^2b-b^3=(2ab-2b^2) are a=b,a=-b+2;\quad b\ne 0

Find the zeros of solvefor a,a^2b-b^3=(2ab-2b^2)

The zeros of solvefor a,a^2b-b^3=(2ab-2b^2) are a=b,a=-b+2;\quad b\ne 0

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solve for

a, a^{2} b - b^{3} = (2 ab - 2 b^{2})

a = b, a = - b + 2; b \neq = 0

Solution steps

a^{2} b - b^{3} = (2 ab - 2 b^{2})

Refine

a^{2} b - b^{3} = 2 ab - 2 b^{2}

Move

2 b^{2}

to the left side

a^{2} b - b^{3} + 2 b^{2} = 2 ab

Move

2 ab

to the left side

a^{2} b - b^{3} + 2 b^{2} - 2 ab = 0

Write in the standard form

a x^{2} + b x + c = 0

b a^{2} - 2 ba - b^{3} + 2 b^{2} = 0

Factor

b a^{2} - 2 ba - b^{3} + 2 b^{2} : b (a - b) (a + b - 2)

b (a - b) (a + b - 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

a - b = 0 or a + b - 2 = 0

Solve

a - b = 0 : a = b

Solve

a + b - 2 = 0 : a = - b + 2

The solutions to the quadratic equation are:

a = b, a = - b + 2; b \neq = 0

- 3 d^{2} - 4 d + 5 = 0

25 r^{2} + 7 = 107

6 x^{2} + 5 x + 8 = 0

a, (a + b)^{3} = a^{3} + b^{3}

x^{2} = 3 x - 4

What are the solutions to the equation solvefor a,a^2b-b^3=(2ab-2b^2) ?
The solutions to the equation solvefor a,a^2b-b^3=(2ab-2b^2) are a=b,a=-b+2;\quad b\ne 0
Find the zeros of solvefor a,a^2b-b^3=(2ab-2b^2)
The zeros of solvefor a,a^2b-b^3=(2ab-2b^2) are a=b,a=-b+2;\quad b\ne 0