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

1 Answer
Apr 12, 2017

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 .