Just factor all;

1) 4x² - 12x =

The GCF is 4x

Dividing (4x² - 12x) / 4x will give you x-3

So, the answer is 4x (x - 3)

2) 9m² - 16n² =

This is a special product called Difference of two squares since 9m² and 16n² are perfect squares.

So, the answer must be (3m - 4n) (3m + 4n)

3) 4a² + 12a + 9 =

This is also another special product called Square of the Sum since it fits the process of it.

So the answer is (2x + 3) (2x + 3)

4) 2x² + 9x - 5 =

I don't see this as a special product but just a factorable equation.

Use 2 [from the 1st term] and 5 [from the last term] as your basis

1, 2 are the factors of 2

1, -1, 5, -5 are the factors of -5

After a lot of Trial and Error.

The factors are (2x - 1) (x + 5)

5) 27x³ - 8y ³ =

This is also a famous special product called as the Differencew of 2 Cubes.

(3x - 2y) (9x² + 6xy + 4y²)

6) a³ + 125b³ =

This is yet another special product called Sum of Two Cubes.

Therefore, the answer should be (a + 5b) (a² - 5ab + 25b)

7) xm + hm - xn - hn =

This can be factored out by using the process called Grouping.

This is to "group" the polynomial into 2 binomials which can be extracted later on.

To use this process you need to group terms with similiar factors.

xm + hm - xn - hn

Grouping this into 2 groups will give

(xm - xn) and (hm - hn)

Now factor out the two

First with (xm - xn)

This will give you x and (m - n)

Now with (hm - hn)

This will give you h and (m - n)

Now see how they are related.

(m - n) is the first factor while combining x and h will give you (x + h) the second factor.

Therefore, (m - n) (x + h) are the factors.

4:2x²+9x-5=

5:27x³-8y³=

Thats the original