Question

Factor the expression completely over the complex numbers. y4+12y2+36

Answer 1

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Heya

y⁴ + 12y² + 36

= (y²)² + 2(y²)(6) + (6)²

Using identity

a² + 2ab + b² = (a + b)²

= (y² + 6)²

Hope this helps you.

Answer 2

Given
y4+12y2+36 = (y^2)^2+2.y^2.6+(6)^2

$= ({y}^{2} + 6) {}^{2}$
$= (y {}^{2} + 6)(y {}^{2} + 6)$
$= (y {}^{2} - (i \sqrt{6}) {}^{2})(y { }^{2} - (i \sqrt{6} ) {}^{2} )$
$= (y + i \sqrt{6} )(y - i \sqrt{6} )(y + i \sqrt{6} )(y - i \sqrt{6} )$
$= (y + i \sqrt{6} ) {}^{2} (y - i \sqrt{6} ) {}^{2}$
hope it helps you