Question

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

Answer 1

Answer:

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

Step-by-step 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)

Answer 2

Answer:

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

Step-by-step explanation:

$x^4+9$

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

Apply the formula for the difference of two squares.

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

$-9=3i^2$

$x^4=(x^2)^2$

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