1. expanding multiplying a term over a bracket.
Recap.

2. Factorise Finding terms that multiply to make an expression
Factorise Finding terms that multiply to make an expression. It is the reverse of expanding.
4a + 3a2
So we are looking for two terms that will multiply together to make this expression. To find those terms we are going to look for what is common to both of them, to look what we can divide both of them by. In this case, we can divide both by a, so we are going to ask, what can we multiply a by, to make each of these terms? The answer is a(4 + 3a). We can check it is correct by expanding.

3. Factorise
15 + 5a
12ab3 + 4a2b

4. Factorise
4a3 + 10a2b
9a3 + 2b
Why is the bottom one not possible?

5. Factorise
3a2 + 8a3b + 4ab
4xy3+ 6xy

6. 6) 6y + 5x2 6a + a2 7) 3ab + 6ab2 12 + 3a 8) 5b2 + 15b 4a2 + 8ab
Factorise
6a + a2
12 + 3a
4a2 + 8ab
9b + 9b3
4xy2 + 2x2y
6) 6y + 5x2
7) 3ab + 6ab2
8) 5b2 + 15b
9) 2a2 + 4a + 6a3
10) ab4 + 4ab2 + 3a3b3

7. answers
6a + a2 = a(6 + a)
12 + 3a = 3(4 + a)
4a2 + 8ab = a(6 + a)
9b + 9b3 = 9b(1 + b)
4xy2 + 2x2y
6) 6y + 5x2 = N/A
7) 3ab + 6ab2
8) 5b2 + 15b
9) 2a2 + 4a + 6a3
10) ab4 + 4ab2 + 3a3b3
= 3ab(1 + 2b)
= 5b(b + 3)
= 2xy(y + 2x)
= 2a(a a2)
= ab(b3 + 4b + 3a2b2)