Factor the expression completely over the complex numbers. y 4 +14 y 2 +49

Given expression : .

Soltution: Let us convert given expression in quadratic form.

y^4 =(y^2)^2.

Given expression could be written in quadratic form as,

(y2)^2 + 2 * (y^2) (7) +(7)^2.

If we compare that above expression by square of the sum identity,

(a)^2 + 2(a)(b) +(b)^2 = (a+b)^2.

We can see that a = y^2, b=7.

Substituting values of a and b in (a+b)^2, we get

Expanding above expression into two factors, we get

But .

We have +7 there.

So, 7=[/tex]

Substituting this value of +7 in expression, we get

Applying difference of the squares identity (n)^2 -(m)^2 = (n-m)(n+m).

Therefore, final factored expression is

21/58.

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