Question

a^3 +2a^2-a-2 factorise​

Answer 1

Answer:

Let us space this out a little bit to make it more accessible.

a^3 - (1/a^3) - 2a + 2/a.

Ok. Let us see if we can see some identities here. (1/a^3) can be written as (1/a)^3. And now we can apply the identity a^3 - b^3 = (a-b)(a^2 + b^2 + ab). And we can also take -2 common out of the last two terms.

a^3 - (1/a)^3 - 2 (a- 1/a)

Apply the a^3 - b^3 identity-

(a - 1/a) ( a^2 + 1/a^2 + a*1/a) - 2(a- 1/a)

So now, we can take the a- 1/a term common out of the two terms.

(a- 1/a) (a^2 + 1/a^2 + 1 -2) and we get-

(a- 1/a) (a^2 + 1/a^2 -1)

There you have it.

Answer 2

Refer to the attached image ❤