How do you factor $- x^{2} y^{2} + x^{4} + 4 y^{2} - 4 x^{2}$ $-x^2y^2 + x^4 + 4y^2 - 4x^2$ ?

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How do you factor $- x^{2} y^{2} + x^{4} + 4 y^{2} - 4 x^{2}$ $-x^2y^2 + x^4 + 4y^2 - 4x^2$ ?

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Answer 1 · 2016-02-02T11:27:08

Combination

Explanation:

We have the equation as

$f (x, y) = - x^{2} y^{2} + x^{4} + 4 y^{2} - 4 x^{2}$ $f(x,y) = -x^2y^2+x^4+4y^2-4x^2$
$= x^{4} - x^{2} y^{2} - 4 x^{2} + 4 y^{2}$ $= x^4-x^2y^2-4x^2+4y^2$
$= x^{2} (x^{2} - y^{2}) - 4 (x^{2} - y^{2})$ $= x^2(x^2-y^2)-4(x^2-y^2)$
$= (x^{2} - y^{2}) \times (x^{2} - 4)$ $= (x^2-y^2)\times (x^2-4)$

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How do you factor $- x^{2} y^{2} + x^{4} + 4 y^{2} - 4 x^{2}$ $-x^2y^2 + x^4 + 4y^2 - 4x^2$ ?

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How do you factor $- x^{2} y^{2} + x^{4} + 4 y^{2} - 4 x^{2}$ $-x^2y^2 + x^4 + 4y^2 - 4x^2$ ?