What is the standard form of #f(x)=x(3x+5)^2 #?

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Answer 1 · 2017-07-30T14:23:28

See a solution process below:

First, expand the squared term using this rule:

#(color(red)(a) + color(blue)(b))^2 = color(red)(a)^2 + 2color(red)(a)color(blue)(b) + color(blue)(b)^2#

Substituting #color(red)(3x)# for #color(red)(a)# and #color(blue)(5)# for #color(blue)(b)# gives:

#f(x) = x(color(red)(3x) + color(blue)(5))^2#

#f(x) = x((color(red)(3x))^2 + (2 * color(red)(3x) * color(blue)(5)) + color(blue)(5)^2)#

#f(x) = x(9x^2 + 30x + 25)#

Now, we can multiply the #x# by each term within the parenthesis:

#f(x) = (x * 9x^2) + (x * 30x) + (x * 25)#

#f(x) = 9x^3 + 30x^2 + 25x#