Question

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

Answer 1

See a solution process below:

Explanation:

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`