What is factor x^4+4x^2*y^2+16y^4 ?

The solution to factor x^4+4x^2*y^2+16y^4 is (x^2+4y^2+2xy)(x^2+4y^2-2xy)

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factor x^4+4x^2*y^2+16y^4

factor

x^{4} + 4 x^{2} \cdot y^{2} + 16 y^{4}

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

Solution steps

x^{4} + 4 x^{2} y^{2} + 16 y^{4}

Add and subtract

4 x^{2} y^{2}

= x^{4} + 8 x^{2} y^{2} + 16 y^{4} - 4 x^{2} y^{2}

Factor

x^{4} + 8 x^{2} y^{2} + 16 y^{4} : (x^{2} + 4 y^{2})^{2}

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

Apply exponent rules

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

Factor

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

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

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

(3 x + 2)^{2} - (3 x - 1)^{2} - 3 (2 x + 1)

(\frac{15}{10 t - 8}) 2

8 x^{2} - 10 x^{4} - 0.342 + 16 x + 114 - 10

3 m^{2} + 5 m + 6 m^{2} + m

What is factor x^4+4x^2*y^2+16y^4 ?
The solution to factor x^4+4x^2*y^2+16y^4 is (x^2+4y^2+2xy)(x^2+4y^2-2xy)