Factorise as far as possible:

1) 2a^2b + 8a^2b^2
The answer i got for this is 2ab(a+4ab). I'm not entirely sure if this is fully factorised or not. Can you please correct me if i am wrong.

2) x^2 + 5x - 6
I'm not sure how i can do this. Can someone please explain how without giving me the answer as i want to learn it properly.

Also can you please give me some more examples that i can work from. Maybe 2 or 3 will be fine.

Thank you :)

I just worked out the second answer. I got

(X-1)(x+6)

Is this also correct?

1) 2a^2b(1+4b)

2) Correct

1) To factorize 2a^2b + 8a^2b^2, we first look for a common factor among the terms. In this case, both terms have a factor of 2ab. So we can write:

2ab(a + 4ab)

This is the fully factorized form. Well done!

2) To factorize x^2 + 5x - 6, we look for two numbers whose product equals -6 and whose sum equals 5. These numbers are 6 and -1. We can then rewrite the middle term 5x as 6x - x:

x^2 + 6x - x - 6

Now we group the terms and factor by grouping:

(x^2 + 6x) - (x + 6)

Now, factor out the common factor from each group:

x(x + 6) - 1(x + 6)

Notice that we now have a common factor of (x + 6). So we can write it as:

(x - 1)(x + 6)

This is the fully factorized form.

Here are a couple more examples for you to practice:

3) Factorize 3x^2 - 12x + 9

4) Factorize 4x^3 - 12x^2 - 5x + 15

Remember to look for common factors, factor by grouping, and use techniques like factoring by grouping or factoring special forms (e.g., a^2 - b^2 = (a + b)(a - b)) to factorize expressions further.