What is the standard form of a polynomial #x(x+5)^2#?

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Answer 1 · 2017-07-24T10:34:45

See a solution process below:

First, expand the terms in parenthesis 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 #x# for #a# and #5# for #b# gives:

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

#x(x^2 + 10x + 25#

Now, we can multiply each term within the parenthesis by the term outside the parenthesis to put the expression in standard polynomial form:

#color(red)(x)(x^2 + 10x + 25) => (color(red)(x) * x^2) + (color(red)(x) * 10x) + (color(red)(x) * 25) =>#

#x^3 + 10x^2 + 25x + 0#