How do you simplify #2(sqrt(5x) - 3)^2#?

1 Answer

Answer:

#10x-12sqrt(5x)+18#

Explanation:

We can rewrite the expression to specifically show all the terms:

#2(sqrt(5x)-3)^2=2(sqrt(5x)-3)(sqrt(5x)-3)#

Let's set aside the leading 2 for a minute and work with the two bracketed terms. We'll use FOIL to handle it:

FOIL

  • #color(red)(F)# - First terms - #(color(red)(a)+b)(color(red)(c)+d)#
  • #color(brown)(O)# - Outside terms - #(color(brown)(a)+b)(c+color(brown)d)#
  • #color(blue)(I)# - Inside terms - #(a+color(blue)b)(color(blue)(c)+d)#
  • #color(green)(L)# - Last terms - #(a+color(green)b)(c+color(green)d)#

This gives us:

  • #color(red)(F)=>sqrt(5x)sqrt(5x)=5x#
  • #color(brown)(O)=>sqrt(5x)(-3)=-3sqrt(5x)#
  • #color(blue)(I)=>(-3)(sqrt(5x))=-3sqrt(5x)#
  • #color(green)(L)=>(-3)(-3)=9#

#5x-3sqrt(5x)-3sqrt(5x)+9=5x-6sqrt(5x)+9#

And so #2(sqrt(5x)-3)^2=2(5x-6sqrt(5x)+9)#

We can now distribute the 2 through the bracket:

#2(5x-6sqrt(5x)+9)=color(blue)(ul(bar(abs(color(black)(10x-12sqrt(5x)+18))))#