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:

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

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

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