Question

factor the expression below 10x³ + 20x² + 10x

Explanation:

Step1: Factor out GCF

Identify and factor out the greatest common factor (GCF) of all terms. The GCF of $10x^3$, $20x^2$, and $10x$ is $10x$.
$10x^3 + 20x^2 + 10x = 10x(x^2 + 2x + 1)$

Step2: Factor quadratic trinomial

Factor the perfect square trinomial $x^2 + 2x + 1$, which follows the pattern $(a+b)^2 = a^2 + 2ab + b^2$ where $a=x$ and $b=1$.
$x^2 + 2x + 1 = (x+1)^2$

Answer:

$10x(x+1)^2$