Question

How do you simplify `(2+sqrtx)(8+sqrtx)`?

Answer 1

`16+10sqrtx+x`

Explanation:

Each term in the second bracket must be multiplied by each term in the first bracket. This can be achieved as follows.

`rArr(color(red)(2+sqrtx))(8+sqrtx)`

`=color(red)(2)(8+sqrtx)color(red)(+sqrtx)(8+sqrtx)`

distribute the brackets.

`rArr16+2sqrtx+8sqrtx+(sqrtx xxsqrtx)`

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(sqrtx xxsqrtx=x)color(white)(2/2)|)))`

collecting like terms and simplifying.

`=16+10sqrtx+x`