What is factor a^2-2a^3b+2ab^3-b^2 ?

The solution to factor a^2-2a^3b+2ab^3-b^2 is (2ab-1)(b+a)(b-a)

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factor a^2-2a^3b+2ab^3-b^2

factor

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

(2 ab - 1) (b + a) (b - a)

Solution steps

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

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

Factor out

- a^{2}

from

- 2 a^{3} b + a^{2} : - a^{2} (2 ab - 1)

Factor out

b^{2}

from

2 a b^{3} - b^{2} : b^{2} (2 ab - 1)

= - a^{2} (2 ab - 1) + b^{2} (2 ab - 1)

Factor out common term

2 ab - 1

= (2 ab - 1) (- a^{2} + b^{2})

Factor

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

= (2 ab - 1) (b + a) (b - a)

\frac{1}{4} x^{3}

5 a^{2} + 13 a - 6

x^{2} \cdot \frac{1}{x ^{2}}

\frac{3}{4} + (- \frac{1}{2})

4 x^{3} 175 x^{3} y^{3}

What is factor a^2-2a^3b+2ab^3-b^2 ?
The solution to factor a^2-2a^3b+2ab^3-b^2 is (2ab-1)(b+a)(b-a)