Question

(b) Factorise fully 2 a²b + 6ab2

Answer 1

Answer:

2ab(a+3b)

Step-by-step explanation:

$2 {a}^{2} b + 6a {b}^{2}$

Factor out common term : 2ab

$2 {a}^{2}b \div 2a = a \\ 6a {b}^{2} \div 2ab = 3b \\ 2ab(a + 3b)$

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.

$\frac{2a^2b+6ab^2}{2ab}\\a+3b$

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)