What is factor x^2-2x*y^2+y^4 ?

The solution to factor x^2-2x*y^2+y^4 is (x-y^2)^2

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factor x^2-2x*y^2+y^4

factor

x^{2} - 2 x \cdot y^{2} + y^{4}

(x - y^{2})^{2}

Solution steps

x^{2} - 2 x y^{2} + y^{4}

Break the expression into groups

= (x^{2} - x y^{2}) + (- x y^{2} + y^{4})

Factor out

x

from

x^{2} - x y^{2} : x (x - y^{2})

Factor out

- y^{2}

from

- x y^{2} + y^{4} : - y^{2} (x - y^{2})

= x (x - y^{2}) - y^{2} (x - y^{2})

Factor out common term

x - y^{2}

= (x - y^{2}) (x - y^{2})

Apply exponent rule:

aa = a^{2}

(x - y^{2}) (x - y^{2}) = (x - y^{2})^{2}

= (x - y^{2})^{2}

2 a^{3} + 6 a^{2} + 6 a + 2

(4^{3} y^{3})^{2}

x^{3} - 63 x - 162

(x + y)^{2} + (x - y)^{3}

\frac{( 3 x )}{( 7 y )} \cdot \frac{( 49 y )}{( 9 x )}

What is factor x^2-2x*y^2+y^4 ?
The solution to factor x^2-2x*y^2+y^4 is (x-y^2)^2