How do you simplify the expression #(5x-2)^2#?

2 Answers
Jun 17, 2017

Answer:

#25x^2-20x+4#

Explanation:

To solve this problem first you rewrite as follows:

#(color(blue)(5x)color(darkred)(-2))(color(red)(5x)color(green)(-2))#

Then you proceed to FOIL it:

Where you multiply the #color(blue)"first term"# with the #color(red)"outer term"# then you multiply the #color(blue)"first term"# with the #color(green)"inner term"#:

#(color(blue)(5x))(color(red)(5x))=25x^2#

#(color(blue)(5x))(color(green)(-2))=-10x#

Now you multiply the #color(darkred)"last term"# with the #color(red)"outer term"# then you multiply the #color(darkred)"last term"# with the #color(green)"inner term"#:

#color(darkred)((-2))(color(red)(5x))=-10x#

#color(darkred)((-2))(color(green)(-2))=4#

Now combine them:

#25x^2-10x-10x+4#

Simplify:

#25x^2-20x+4#

Jun 17, 2017

Answer:

#25x^2-20x+4#

Explanation:

#"express " (5x-2)^2" as " (5x-2)(5x-2)#

#"each term in the second bracket is multiplied by each term in"#
#"the first bracket"#

#(color(red)(5x-2))(5x-2)#

#=color(red)(5x)(5x-2)color(red)(-2)(5x-2)#

#=(color(red)(5x)xx5x)+(color(red)(5x)xx-2)+(color(red)(-2)xx5x)+(color(red)(-2)xx-2)#

#=25x^2+(-10x)+(-10x)+4#

#=25x^2-10x-10x+4#

#=25x^2-20x+4#