Question

1. $21x^2y^4 - 14xy^2$
2. $6x^4y^5 - 18x^2y^7$
3. $8x^3 + 12x^2 - 4x$
4. $16m^3 - 8m^2 + 12m$

Explanation:

Step1: Factor out GCF for #17

Find GCF of $21x^2y^4$ and $14xy^2$: $\text{GCF}=7xy^2$

$$\begin{align} 21x^2y^4 - 14xy^2 &= 7xy^2(3xy^2 - 2) \end{align}$$

Step2: Factor out GCF for #18

Find GCF of $6x^4y^5$ and $18x^2y^7$: $\text{GCF}=6x^2y^5$

$$\begin{align} 6x^4y^5 - 18x^2y^7 &= 6x^2y^5(x^2 - 3y^2) \end{align}$$

Step3: Factor out GCF for #20

Find GCF of $8x^3$, $12x^2$, $-4x$: $\text{GCF}=4x$

$$\begin{align} 8x^3 + 12x^2 - 4x &= 4x(2x^2 + 3x - 1) \end{align}$$

Step4: Factor out GCF for #21

Find GCF of $16m^3$, $-8m^2$, $12m$: $\text{GCF}=4m$

$$\begin{align} 16m^3 - 8m^2 + 12m &= 4m(4m^2 - 2m + 3) \end{align}$$

Answer:

1. $7xy^2(3xy^2 - 2)$
2. $6x^2y^5(x^2 - 3y^2)$
3. $4x(2x^2 + 3x - 1)$
4. $4m(4m^2 - 2m + 3)$