Question

Problem

Answer 1

a. $x^4 + 4x^2 + 4$

b. x = ∛-1 and -3

How to expand the expression

a.  Given

(x² + 2)²

First, we open up the bracket

$(x^2 + 2) (x^2 + 2)$

Multiply through

$x^4 + 2x^2 + 2x^2 + 4$

Collect like terms

$x^4 + 4x^2 + 4$

b. Let's factorize

$x^4 + 4x + 3$

Find the factors of 3 that are products of 4, they are 3 and 1

Use it to replace 4x as 3x and x

$x^4 + 3x + x + 3$

Let's make the expression two

$(x^4 + 3x) (x+ 3)$

Find the common factor

$x^3(x + 3)+ 1(x+ 3)$

So,

$x^3 + 1 = 0$ and $x + 3 = 0$

$x = 3\sqrt{-1}$ and x = -3

Thus, x = ∛-1 and -3

Learn more about factorization here:

brainly.com/question/25829061

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