Question

How do you simplify `(4sqrtx+1)(3sqrtx+2)`?

Answer 1

See a solution process below:

Explanation:

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

`(color(red)(4sqrt(x)) + color(red)(1))(color(blue)(3sqrt(x) + color(blue)(2))` becomes:

`(color(red)(4sqrt(x)) xx color(blue)(3sqrt(x))) + (color(red)(4sqrt(x)) xx color(blue)(2)) + (color(red)(1) xx color(blue)(3sqrt(x))) + (color(red)(1) xx color(blue)(2))`

`12(sqrt(x))^2 + 8sqrt(x) + 3sqrt(x) + 2`

`12x + 8sqrt(x) + 3sqrt(x) + 2`

We can now combine like terms:

`12x + (8 + 3)sqrt(x) + 2`

`12x + 11sqrt(x) + 2`