Question

How do you simplify `(0.1x + 0.4y)^2`?

Answer 1

See the entire solution process below:

Explanation:

We can rewrite this expression as:

`(0.1x + 0.4y)(0.1x + 0.4y)`

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

`(color(red)(0.1x) + color(red)(0.4y))(color(blue)(0.1x) + color(blue)(0.4y))` becomes:

`(color(red)(0.1x) xx color(blue)(0.1x)) + (color(red)(0.1x) xx color(blue)(0.4y)) + (color(red)(0.4y) xx color(blue)(0.1x)) + (color(red)(0.4y) xx color(blue)(0.4y))`

`0.01x^2 + 0.04xy + 0.04xy + 0.16y^2`

We can now combine like terms:

`0.01x^2 + (0.04 + 0.04)xy + 0.16y^2`

`0.01x^2 + 0.08xy + 0.16y^2`