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

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Answer 1 · 2017-06-26T02:11:04

See a solution process below:

First, expand the "#(x + 2)^2#" term using this rule for polynomials:

#(a + b)^2 = a^2 + 2ab + b^2#

Substituting:

#x# for #a#

#2# for #b#

Gives:

#x(x + 2)^2 = x(x^2 + (2x * 2) + 2^2) => x(x^2 + 4x + 4)#

Now, expand the terms within parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis:

#color(red)(x)(x^2 + 4x + 4) => (color(red)(x) xx x^2) + (color(red)(x) xx 4x) + (color(red)(x) xx 4) =>#

#x^3 + 4x^2 + 4x#