Question

PLEASSE HELP MEEEEE!!!

Answer 1

(y^2+20)^2

you have to factor by grouping the expression

Answer 2

`\sf (y^2 + 20)^2 \textsf{ Or } (y^2 + 20)(y^2 + 20)`

Explanation:

To factor the expression y⁴ + 40y² + 400 completely over the complex numbers, we can use a substitution to simplify it.

Let z = y². Then the expression becomes:

z² + 40z + 400

Now, factor this quadratic expression:

`\sf z^2 + 2 \cdot z \cdot 40 + 40^2`

We have formula: (a+b)² = a²+2ab + b², Using this, we get

`\sf (z + 20)^2`

Now, substitute back the original variable:

`\sf (y^2 + 20)^2`

So, the factored expression over the complex numbers is:

`\sf (y^2 + 20)^2 \textsf{ Or } (y^2 + 20)(y^2 + 20)`