How do you multiply #(3x- 1)^2#?

1 Answer
Jul 24, 2017

Answer:

See a solution process below:

Explanation:

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#