Question

question
factor the expression completely.
$x^2y^3 + y^4$

Explanation:

Step1: Identify the GCF

Find the greatest common factor (GCF) of the two terms \(x^{2}y^{3}\) and \(y^{4}\). The GCF of the coefficients (both 1) is 1, and the GCF of the variables is \(y^{3}\) (since \(y^{3}\) is the highest power of \(y\) that divides both terms).

$$ \text{GCF} = y^{3} $$

Step2: Factor out the GCF

Factor out \(y^{3}\) from each term in the expression \(x^{2}y^{3}+y^{4}\).

$$ x^{2}y^{3}+y^{4}=y^{3}(x^{2}) + y^{3}(y) $$

Using the distributive property \(ab + ac=a(b + c)\), we get:

$$ y^{3}(x^{2}+y) $$

Answer:

\(y^{3}(x^{2}+y)\)