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

1 Answer
Apr 12, 2017

Answer:

# 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 #.