Question

(b) Factorise fully 2 a²b + 6ab2

Answer 1

2ab(a+3b)

Explanation:

`2 {a}^(2) b + 6a {b}^(2)`

Factor out common term : 2ab

`2 {a}^(2)b / 2a</strong><strong> = a \\ 6a {b}^(2) / 2ab = 3b \\ 2ab(a + 3b)`

Answer 2

`2a^2b+6ab^2`

Perhaps, you mean 6ab² (If not please remind me.)

Factoring the polynomials can be done by pulling out the terms that can be divided by that terms.

For example,
`2x^2+4` We can divide the whole polynomial by 2. Thus, we factor 2 out of the polynomial as we get
`2(x^2+2)` -- Factoring is like dividing, but instead - we pull them out.

Now let's get back to the question.

Notice that the polynomial can be divided by 2, a and b.

So we pull 2, a and b out of the polynomial and divide them.

`(2a^2b+6ab^2)/(2ab)\\a+3b`

When dividing, we should get a + 3b.

Then we pull out 2ab outside the bracket.

`2ab(a+3b)`

Thus, the answer is 2ab(a+3b)