Final answer:
This detailed answer explains how to factorize various expressions step by step, providing examples for each case.
Step-by-step explanation:
1) 6x + 4
We can factor out a 2 from both terms, giving us 2(3x + 2).
2) 6y^2 - 4y
In this case, we can factor out a common factor of 2y, giving us 2y(3y - 2).
3) 10xy + 5xz
Here, we can factor out 5x, resulting in 5x(2y + z).
4) 3x^2y - 9x^3y^3
In this case, we can factor out a common factor of 3xy, giving us 3xy(x - 3xy^2).
5) 8a^3bc - 12ab^3cd + 4b^4c^2d^2
We can factor out 4abcd, resulting in 4abcd(2a^2 - 3b^2c + bcd).
6) 6z^2t^3 + 3zst^4 - 12z^2t^3
Here, we can factor out a common factor of 3zt^3, giving us 3zt^3(2z - s + 4z).