Question

simplify the following expression.

\\(x^2 + 4x + 3)^2\\

Explanation:

Identify the expression and method

Using the Trinomial Squaring knowledge point

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

For the expression \((x^2 + 4x + 3)^2\), we define:

$$ a = x^2, \quad b = 4x, \quad c = 3 $$

Expand the squared terms

Using the Trinomial Squaring knowledge point

$$
LATEXBLOCK0
$$

Expand the cross-product terms

Using the Trinomial Squaring knowledge point

$$
LATEXBLOCK1
$$

Combine and simplify like terms

Using the Polynomial Simplification knowledge point

$$
LATEXBLOCK2
$$

Answer:

\(x^4 + 8x^3 + 22x^2 + 24x + 9\)