Question

X^4+9 which pattern can we use to factor the expression?

Answer 1

`\left(x^2+3i\right)\left(x^2-3i\right)`

Explanation:

`x^4+9`

`x^4+9` can be written as
`x^4--9`.

Apply the formula for the difference of two squares.

`(a^2-b^2)=(a+b)(a-b)`

`-9=3i^2`

`x^4=(x^2)^2`

`(x^2)^2-(3i)^2=(x^2+3i)(x^2-3i)`

Answer 2

(x^2 - 3i) ( x^2 +3i)

Explanation:

X^4+9

x^4 - -9

This is the difference of squares (a^2 - b^2) = (a-b)(a+b)

(x^2) ^2 - ( 3i)^2

(x^2 - 3i) ( x^2 +3i)