Question

1. $35n^{4}m^{3} + 25n^{3}m - 25n^{2}m^{2} + 20n$
2. $10u^{2}v^{3} - 5u^{4} + 45u^{2}v - 5u^{3}$
3. $6m^{3}p + 9m^{2}pq$

$3m^{2}p(2m + 3q)$

1. $15p^{2}q^{2}r^{3} + 25p^{2}qr - 30p^{2}q$

Explanation:

Problem 17:

Step1: Find the GCF of terms

The terms are \(35n^4m^3\), \(25n^3m\), \(-25n^2m^2\), \(20n\). The GCF of coefficients \(35,25, - 25,20\) is \(5\), and the GCF of variables is \(n\) (since \(n\) is the lowest power of \(n\) present in all terms). So GCF is \(5n\).

Step2: Factor out GCF

Factor out \(5n\) from each term:
\[

$$\begin{align*} &35n^4m^3+25n^3m - 25n^2m^2+20n\\ =&5n(7n^3m^3 + 5n^2m-5nm^2 + 4) \end{align*}$$

\]

Problem 18:

Step1: Find the GCF of terms

The terms are \(10u^2v^3\), \(-5u^4\), \(45u^2v\), \(-5u^3\). The GCF of coefficients \(10,-5,45,-5\) is \(5\), and the GCF of variables is \(u^2\) (lowest power of \(u\) in all terms). So GCF is \(5u^2\).

Step2: Factor out GCF

Factor out \(5u^2\) from each term:
\[

$$\begin{align*} &10u^2v^3-5u^4 + 45u^2v-5u^3\\ =&5u^2(2v^3 - u^2+9v - u) \end{align*}$$

\]

Problem 19:

Step1: Find the GCF of terms

The terms are \(6m^3p\) and \(9m^2pq\). The GCF of coefficients \(6,9\) is \(3\), and the GCF of variables is \(m^2p\) (lowest power of \(m\) and \(p\) in both terms). So GCF is \(3m^2p\).

Step2: Factor out GCF

Factor out \(3m^2p\) from each term:
\[

$$\begin{align*} &6m^3p + 9m^2pq\\ =&3m^2p(2m+3q) \end{align*}$$

\]

Problem 20:

Answer:

s:

1. \(\boldsymbol{5n(7n^3m^3 + 5n^2m-5nm^2 + 4)}\)
2. \(\boldsymbol{5u^2(2v^3 - u^2+9v - u)}\)
3. \(\boldsymbol{3m^2p(2m + 3q)}\)
4. \(\boldsymbol{5p^2q(3qr^3 + 5r-6)}\)