You can just 1) multiply the binomial by itself, or you can use 2) the square of a binomial pattern. I'll show it to you both ways.
1) Multiply the binomial by itself.
(3x - 2)^2 = (3x - 2)(3x - 2) =
Multiply every term of the first binomial by every term of the second binomial, then collect like terms. (This is often called using FOIL.)
= 9x^2 - 6x - 6x + 4
= 9x^2 - 12x + 4
2) Use the square of a binomial pattern
The square of a binomial is
(a - b)^2 = a^2 - 2ab - b^2
a^2 is the square of the first term.
b^2 is the square of the second term.
-2ab is the product of the two terms and 2.
You have
(3x - 2)^2,
where the first term is 3x, and the second term is -2
square the first term: 9x^2
square the last term: 4
the product of the terms and 2 is: -12x
Put it all together, and you get
9x^2 - 12x + 4
just like we got above with the other method.
