Question

How do you find the product of `(9x + 4)^2`?

Answer 1

`81x^2 + 72x + 16`

Explanation:

To simplify this expression, or any expression, a good start would be writing it out completely and getting rid of the exponent. This will make it a lot easier to multiply.

`(9x + 4)^2` will become `(9x + 4)(9x + 4)`

Now we can begin to multiply by using the FOIL method.

Take the `color(blue)"first term in the first binomial"` and multiply it with `color(green)"every term in the second binomial"`.

Then take the `color(red)"second term in the binomial"` and multiply it with `color(green)"every term in the second binomial"`.

`(9x + 4)(9x + 4)`

`(color(blue)(9x) + 4)(color(green)(9x) + 4)` `color(orange)(->) 9x * 9x color(orange)(->) color(red)(81x^2)`

`(color(blue)(9x) + 4)(9x` `color(green)( + 4))` `color(orange)(->) 9x * 4 color(orange)(->) color(red)(36x)`

`(9x` `color(red)( + 4))(color(green)(9x) + 4)` `color(orange)(->) 4 * 9x color(orange)(->) color(red)(36x)`

`(9x` `color(red)( + 4))(9x` `color(green)( + 4))` `color(orange)(->) 4 * 4 color(orange)(->) color(red)(16)`

Now all we have to do is add the terms that we got and simplify.

`81x^2 + 36x +36x + 16`
`81x^2 + 72x + 16`

As you can see, when we simplify our initial expression, we get our answer which is `81x^2 + 72x + 16`.