a. [tex]x^4 + 4x^2 + 4[/tex]
b. x = ∛-1 and -3
How to expand the expression
a. Given
(x² + 2)²
First, we open up the bracket
[tex](x^2 + 2) (x^2 + 2)[/tex]
Multiply through
[tex]x^4 + 2x^2 + 2x^2 + 4[/tex]
Collect like terms
[tex]x^4 + 4x^2 + 4[/tex]
b. Let's factorize
[tex]x^4 + 4x + 3[/tex]
Find the factors of 3 that are products of 4, they are 3 and 1
Use it to replace 4x as 3x and x
[tex]x^4 + 3x + x + 3[/tex]
Let's make the expression two
[tex](x^4 + 3x) (x+ 3)[/tex]
Find the common factor
[tex]x^3(x + 3)+ 1(x+ 3)[/tex]
So,
[tex]x^3 + 1 = 0[/tex] and [tex]x + 3 = 0[/tex]
[tex]x = 3\sqrt{-1}[/tex] and x = -3
Thus, x = ∛-1 and -3
Learn more about factorization here:
https://brainly.com/question/25829061
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