Question

How do you find the product of `(5x^2 + 3y + 5) (y+9)`?

Answer 1

`5x^2y+45x^2+3y^2+32y+45`

Explanation:

Let's multiply `5x^2` with `y`, `5x^2` with `9`, `3y` with `y`, `3y` with `9`, `5` with `y`, and `5` with `9`.

`5x^2y`
`45x^2`
`3y^2`
`27y`
`5y`
`45`

Simplifying these,

`5x^2y+45x^2+3y^2+32y+45`

(`32y` because the `27y` and `5y` are like terms, and adds up to `32y`)

Answer 2

`color(green)(3y^2+32y+5yx^2+45x^2+45`

Explanation:

`(5x^2+3y+5)(y+9)`

`color(white)(aaaaaaaaaaaaa)` `5x^2+3y+5`
`color(white)(aaaaaaaaaaa)` `xx underline(y+9)`
`color(white)(aaaaaaaaaaaaa)` `5yx^2+3y^2+5y`
`color(white)(aaaaaaaaaaaaaaaaaa)` `45x^2+27y+45`
`color(white)(aaaaaaaaaaaaa)` `overline(5yx^2+45x^2+3y^2+32y+45)`

`color(white)(aaaaaaaaaaaaa)` `color(green)(3y^2+32y+5yx^2+45x^2+45`