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

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

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

factor

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

(\frac{x}{2} + \frac{y}{5})^{3}

144 x^{2} y^{2} + 24 x y + 1

9 y^{3} - 6

5 (4 - 2 x)

^{'} (cos (x) \cdot cos (500 \cdot x) + ∣ x ∣ - 0.4) \cdot ((3 - x \cdot x)^{0.1})^{'}

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