What is factor x^4+3x^2*y^2+4y^4 ?

The solution to factor x^4+3x^2*y^2+4y^4 is (x^2+2y^2+xy)(x^2+2y^2-xy)

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factor x^4+3x^2*y^2+4y^4

factor

x^{4} + 3 x^{2} \cdot y^{2} + 4 y^{4}

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

Solution steps

x^{4} + 3 x^{2} y^{2} + 4 y^{4}

Add and subtract

x^{2} y^{2}

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

Factor

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

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

Factor

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

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

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

(\frac{x}{2} - \frac{y}{5})^{2}

x^{2} - y^{2} + 2 y - 1

1 0^{\frac{1}{2}} \cdot 1 0^{\frac{1}{4}}

x \cdot y^{4} - x^{3}

What is factor x^4+3x^2*y^2+4y^4 ?
The solution to factor x^4+3x^2*y^2+4y^4 is (x^2+2y^2+xy)(x^2+2y^2-xy)