Question

1. $2x^2 = 18x^2y$
2. $18n^2y + 10$
3. $56a^2b + 63ab + 21$
4. $42y^5x^3 + 54y^3x^4 + 6y^2$
5. $30 + 24b^3 + 36a^2b^2$
6. $-54xy + 12x^2 - 6x$
7. $35n^4m^3 + 25n^3m - 25n^2m^2 + 20n$
8. $10u^2v^3 - 5u^4 + 45u^2v - 5u^3$
9. $6m^3p + 9m^2pq$
10. $15p^2q^2r^3 + 25p^2qr - 30p^2q$

Explanation:

Let's solve problem 19: \(6m^{3}p + 9m^{2}pq\)

Step 1: Identify the GCF

Find the greatest common factor (GCF) of the coefficients and the variables.

• Coefficients: GCF of 6 and 9 is 3.
• Variables: For \(m\), the lowest power is \(m^{2}\); for \(p\), the lowest power is \(p\); \(q\) appears only in the second term, so not in GCF.

So GCF is \(3m^{2}p\).

Step 2: Factor out the GCF

Divide each term by \(3m^{2}p\) and write the expression as the product of GCF and the remaining polynomial.
\(6m^{3}p\div3m^{2}p = 2m\)
\(9m^{2}pq\div3m^{2}p = 3q\)
So, \(6m^{3}p + 9m^{2}pq = 3m^{2}p(2m + 3q)\)

Answer:

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