Question

\\x^4 + 4x^2 + 4\\

Explanation:

Identify the expression structure

Using the Factoring Trinomials knowledge point

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

Apply substitution for quadratic form

Using the Factoring Trinomials knowledge point

$$ \text{Let } u = x^2. \text{ Then } u^2 = x^4. $$

$$ u^2 + 4u + 4 $$

Factor the quadratic expression

Using the Square of a Binomial Sum knowledge point

$$ u^2 + 4u + 4 = (u + 2)^2 $$

Substitute back the original variable

Using the Factoring Trinomials knowledge point

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

Answer:

Factor the expression: <blank>\((x^2 + 2)^2\)</blank>