Sure, let's simplify these expressions step-by-step:
### 2. [tex]\(4x - 8y\)[/tex]
This expression is already in its simplest form:
[tex]\[
4x - 8y
\][/tex]
### 4. [tex]\(10x - 15x^2\)[/tex]
Factor out the greatest common divisor (GCD) which is [tex]\(5x\)[/tex]:
[tex]\[
10x - 15x^2 = 5x(2 - 3x)
\][/tex]
### 6. [tex]\(4m^2 - 20am\)[/tex]
Factor out the GCD which is [tex]\(4m\)[/tex]:
[tex]\[
4m^2 - 20am = 4m(m - 5a)
\][/tex]
### 8. [tex]\(ax + bx + cx\)[/tex]
Factor out the common term [tex]\(x\)[/tex]:
[tex]\[
ax + bx + cx = x(a + b + c)
\][/tex]
### 10. [tex]\(4a^3bx - 4bx\)[/tex]
Factor out the common term [tex]\(4bx\)[/tex]:
[tex]\[
4a^3 bx - 4bx = 4bx(a^3 - 1)
\][/tex]
### 12. [tex]\(3ab + 6ac - 9ad\)[/tex]
Factor out the GCD which is [tex]\(3a\)[/tex]:
[tex]\[
3ab + 6ac - 9ad = 3a(b + 2c - 3d)
\][/tex]
### 14. [tex]\(6x^4 - 30x^3 + 2x^2\)[/tex]
Factor out the GCD which is [tex]\(2x^2\)[/tex]:
[tex]\[
6x^4 - 30x^3 + 2x^2 = 2x^2(3x^2 - 15x + 1)
\][/tex]
### 16. [tex]\(12m^2n + 24m^3n^2 - 36m^4n^3\)[/tex]
Factor out the GCD which is [tex]\(12m^2n\)[/tex]:
[tex]\[
12m^2n + 24m^3n^2 - 36m^4n^3 = 12m^2n(1 + 2mn - 3m^2n^2)
\][/tex]
### 18. [tex]\(10p^2q^3 + 14p^3q^2 - 18p^4q^3 - 16p^5q^4\)[/tex]
Factor out the GCD which is [tex]\(p^2q^2\)[/tex]:
[tex]\[
10p^2q^3 + 14p^3q^2 - 18p^4q^3 - 16p^5q^4 = p^2q^2(10q + 14p - 18p^2q - 16p^3q^2)
\][/tex]
So, the simplified forms of the given expressions are:
1. [tex]\(4x - 8y\)[/tex]
2. [tex]\(5x(2 - 3x)\)[/tex]
3. [tex]\(4m(m - 5a)\)[/tex]
4. [tex]\(x(a + b + c)\)[/tex]
5. [tex]\(4bx(a^3 - 1)\)[/tex]
6. [tex]\(3a(b + 2c - 3d)\)[/tex]
7. [tex]\(2x^2(3x^2 - 15x + 1)\)[/tex]
8. [tex]\(12m^2n(1 + 2mn - 3m^2n^2)\)[/tex]
9. [tex]\(p^2q^2(10q + 14p - 18p^2q - 16p^3q^2)\)[/tex]
