How do you multiply #(2a+3b)^2#?

1 Answer

Answer:

Expand out the square so it's easier to see, then use the distributive property to arrive at
#4a^2+12ab+9b^2#

Explanation:

Let's first expand this out so that it's easier to see and work with:

#(2a+3b)^2#
#(2a+3b)(2a+3b)#

Now we use the distributive property which says that each term in the first bracket multiplies against each term in the second bracket, like this:

#2a*2a=4a^2#
#2a*3b=6ab#
#3b*2a=6ab#
#3b*3b=9b^2#

And now we add them all up

#4a^2+6ab+6ab+9b^2#

We can combine the 2 #6ab# terms to arrive at

#4a^2+12ab+9b^2#