Question

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

Answer 1

See a solution process below:

Explanation:

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`