Question

How do you multiply `(3x + 9)(2x + 5)`?

Answer 1

`(3x+9)(2x+5)=6x^2+33x+45`

Explanation:

If you find it helpful then you can use the FOIL mnemonic to help collate all the combinations to multiply and add...

`(3x+9)(2x+5) = overbrace(3x*2x)^"First" + overbrace(3x*5)^"Outside"+overbrace(9*2x)^"Inside"+overbrace(9*5)^"Last"`

`color(white)((3x+9)(2x+5)) =6x^2+15x+18x+45`

`color(white)((3x+9)(2x+5)) =6x^2+33x+45`

Answer 2

Another way of showing the same thing:

`6x^2+33x+45`

Explanation:

`color(blue)((3x+9))color(brown)((2x+5))`

Multiply everything inside the right hand side bracket by everything inside the left. Note that the signs follow the value they relate to. So the plus in `+9` follows the 9 and the plus (understood) in `+3x` follows the `3x`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(brown)( color(blue)(3x)(2x+5)" "color(blue)(+9)(2x+5))`

`6x^2+15x" "+18x+45`

`6x^2+33x+45`