Question

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!

Factor the expression over the complex numbers.

y2 + 49

Answer 1

`Use\\\\a^2-b^2=(a-b)(a+b)\\\\i=√(-1)\to i^2=-1\\\\y^2+49=y^2+7^2=y^2-(-1)(7^2)=y^2-(7i)^2\\\\=(y-7i)(y+7i)`

Answer 2

`y^2+49=(y-7i)(y+7i)`

Explanation:

Given : Expression
`y^2+49`

To find : Factor the expression over the complex numbers ?

Solution :

To factor the expression we equate it to zero and find the values of y,

`y^2+49=0`

Subtract 49 both side,

`y^2=-49`

Taking root both side,

`y=√(-49)`

We know,
`√(-1)=i,\ √(49)=7`

`y=\pm 7i`

The factors are
`(y-7i)(y+7i)`

Therefore,
`y^2+49=(y-7i)(y+7i)`