Question

How do you simplify `(u + 7v ) ^ { 2}`?

Answer 1

`u^2+14uv+49v^2`

Explanation:

`(color(blue)(u)color(darkred)(+7v))(color(red)(u)color(green)(+7v))`

You proceed to FOIL it:

Where you multiply the `color(blue)"first term"` with the `color(red)"outer term"` then you multiply the `color(blue)"first term"` with the `color(green)"inner term"`:

`(color(blue)(u))(color(red)(u))=u^2`

`(color(blue)(u))(color(green)(7v))=7uv`

Now you multiply the `color(darkred)"last term"` with the `color(red)"outer term"` then you multiply the `color(darkred)"last term"` with the `color(green)"inner term"`:

`color(darkred)((7v))(color(red)(u))=7uv`

`color(darkred)((7v))(color(green)(7v))=49v^2`

Now combine them:

`u^2+7uv+7uv+49v^2`

Simplify:

`u^2+14uv+49v^2`