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}

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

\frac{1}{2} x^{2} + 1 = 3

(30 + x) (35 + x) = 1300

0 = - x^{2} + 42 x - 20

m^{2} - m + 3 = 0

0 = - x^{2} - 3 x

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