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

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

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

factor

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

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

Solution steps

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

Add and subtract

x^{2} y^{2}

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

Factor

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

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

Apply exponent rule:

a^{m} b^{m} = (ab)^{m}

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

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

Factor

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

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

4 a^{2} - 9 b^{2} - 2 a - 3 b

3 a^{12} + 1 + 3 a^{6} + a^{18}

(6 + x)^{3}

(a + b)^{3} + 1

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

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