Question

\\((x^2 + 4x + 1)^2\\)

Explanation:

Identify the expression and target operation

We are given the expression \((x^2 + 4x + 1)^2\). The goal is to expand and simplify this squared trinomial.

Apply the trinomial squaring formula

Using the Trinomial Squaring knowledge point

$$ (a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca $$

$$
LATEXBLOCK0
$$

$$ (x^2 + 4x + 1)^2 = (x^2)^2 + (4x)^2 + (1)^2 + 2(x^2)(4x) + 2(4x)(1) + 2(1)(x^2) $$

Expand each individual term

Using the Trinomial Squaring knowledge point

$$
LATEXBLOCK1
$$

Combine like terms and arrange in descending order

Using the Polynomial Simplification knowledge point

$$
LATEXBLOCK2
$$

Answer:

\(x^4 + 8x^3 + 18x^2 + 8x + 1\)