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

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

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

factor

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

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

Solution steps

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

Factor

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

= (x^{2} + 2 y^{2})^{2} - 16

Factor the number:

16 = 4^{2}

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

Apply Difference of Two Squares Formula:

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

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

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

Apply rule:

(a) = a

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

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

(3 x y + 4)^{3}

(a - 7) (a + 7)

y + cos (y^{'} (t)) - 0

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

(4^{\frac{m + 1}{4}} \cdot 2 2^{m} 2 2^{- m})^{1} m

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