Question

Factorise 9(a+b)^2 + (a+b) -8 ​

Answer 1

`(9a+9b-8)(a+b+1)`

Explanation:

`9(a+b)^2 + (a+b)-8`

Expand
`(a+b)^2`

`9(a^2+2ab+b^2)+a+b-8`

`9a^2+18ab+9b^2+a+b-8`

Now it is time to think.

Once

`9a^2=9a \cdot a`

`9b^2=9b \cdot b`

`18ab=9ab+9ab`

`-8=-8 \cdot 1`

We can get something in the format

`(9a+9b-8)(\text{some expression here})`

From the conclusions above,

`(9a+9b-8)(a+b+1)`