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.