Question

What is the standard form of a polynomial `6x(x^2+2x+1)`?

Answer 1

`6x^3+12x^2+6x`

Explanation:

`1`. Use the distributive property, `color(red)a(color(blue)b` `color(violet)(+c))=color(red)acolor(blue)b` `color(red)(+a)color(violet)c`, to multiply `6x` by each term within the brackets.

`color(red)(6x)(color(blue)(x^2)` `color(violet)(+2x)` `color(darkorange)(+1))`

`=color(red)(6x)(color(blue)(x^2))color(red)(+6x)(color(violet)(2x))color(red)(+6x)(color(orange)1)`

`2`. Simplify.

`=color(green)(|bar(ul(color(white)(a/a)6x^3+12x^2+6xcolor(white)(a/a)|)))`