Factor
1. 6y + 18y2
2. 5a2 - 25 a3
3. 3m - 9m2 + 15m3
4. 12k2 - 48k4 - 18k6
In each of them, find some factor all the terms have in common.
Take #2 for example:
5a^2 - 25a^3
Well, both divide by 5, so we have:
5(a^2 - 5a^3)
but we can also take a^2 out of the expression inside the brackets:
(a^2 - 5a^3) = a^2*1 - a^2 * 5a
= a^2(1 - 5a)
So the whole thing becomes:
5a^2 (1 - 5a)
Try the first one, and the others, yourself, and ask for more help if you need it!
To factor these expressions, we will look for common factors in each term and then factor them out.
1. 6y + 18y^2
In this expression, the common factor is 6y.
So we can factor it as: 6y(1 + 3y)
2. 5a^2 - 25a^3
Here, the common factor is 5a^2.
We can factor it as: 5a^2(1 - 5a)
3. 3m - 9m^2 + 15m^3
In this expression, there is no common factor among all the terms.
So we can only factor out common factors from pairs of terms.
Let's factor out 3m: 3m(1 - 3m + 5m^2)
4. 12k^2 - 48k^4 - 18k^6
In this expression, the common factor is 6k^2.
We can factor it as: 6k^2(2 - 8k^2 - 3k^4)
Remember, when factoring, it's important to look for common factors in each term and then factor them out.