Question

factor completely. \\(-29x^4y^2 + 21x^8y^3z^3\\)

Explanation:

Step1: Identify the GCF of the terms

The terms are \(-29x^{4}y^{2}\) and \(21x^{8}y^{3}z^{3}\). The GCF of the coefficients \(-29\) and \(21\) is \(1\) (since they are coprime). For the variables, the GCF of \(x^{4}\) and \(x^{8}\) is \(x^{4}\), the GCF of \(y^{2}\) and \(y^{3}\) is \(y^{2}\), and there is no common factor for \(z\) in the first term. So the GCF of the two terms is \(x^{4}y^{2}\).

Step2: Factor out the GCF

Factor out \(x^{4}y^{2}\) from \(-29x^{4}y^{2}+21x^{8}y^{3}z^{3}\):
\[

$$\begin{align*} -29x^{4}y^{2}+21x^{8}y^{3}z^{3}&=x^{4}y^{2}(-29)+x^{4}y^{2}(21x^{4}yz^{3})\\ &=x^{4}y^{2}(-29 + 21x^{4}yz^{3}) \end{align*}$$

\]

Answer:

\(x^{4}y^{2}(-29 + 21x^{4}yz^{3})\)