Use this rule to multiply this expression:
#(color(red)(a) - color(blue)(b))^2 = color(red)(a)^2 - 2color(red)(a)color(blue)(b) + color(blue)(b)^2#
Substituting #3x# for #a# and #1# for #b# gives:
#(color(red)((3x)) - color(blue)(1))^2 => color(red)((3x))^2 - (2 * color(red)(3x) * color(blue)(1)) + color(blue)(1)^2 => #
#9x^2 - 6x + 1#
Another method is to first rewrite the expression as:
#(3x - 1)(3x - 1)#
To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.
#(color(red)(3x) - color(red)(1))(color(blue)(3x) - color(blue)(1))# becomes:
#(color(red)(3x) xx color(blue)(3x)) - (color(red)(3x) xx color(blue)(1)) - (color(red)(1) xx color(blue)(3x)) + (color(red)(1) xx color(blue)(1))#
#9x^2 - 3x - 3x + 1#
We can now combine like terms:
#9x^2 + (-3 - 3)x + 1#
#9x^2 + (-6)x + 1#
#9x^2 - 6x + 1#
