Question

How do you multiply `(x^2 + 3x)(x + 1)`?

Answer 1

`x^3+4x^2+3x`

Explanation:

multiplying out:

`x^3+3x^2+x^2+3x=x^3+4x^2+3x`

Answer 2

`x^3+4x^2+3x`

Explanation:

`"each term in the second factor is multiplied by each term"`
`"in the first factor"`

`(color(red)(x^2+3x))(x+1)`

`=color(red)(x^2)(x+1)color(red)(+3x)(x+1)larrcolor(blue)"distribute"`

`=(color(red)(x^2)xx x)+(color(red)(x^2)xx1)+(color(red)(3x)xx x)+(color(red)(3x)xx1)`

`=x^3color(blue)(+x^2)color(blue)(+3x^2)+3xlarrcolor(magenta)"collect like terms"`

`=x^3+4x^2+3x`