Question

How do you multiply `(2t + 3)(3t - 5)`?

Answer 1

`6t^2-t-15`

Explanation:

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

`rArr(color(red)(2t+3))(3t-5)`

`=color(red)(2t)(3t-5)color(red)(+3)(3t-5)larrcolor(blue)"distribute"`

`=(color(red)(2t)xx3t)+(color(red)(2t)xx-5)+(color(red)(3)xx3t)+(color(red)(3)xx-5)`

`=6t^2color(magenta)(-10t)color(magenta)(+9t)-15larrcolor(blue)"collect like terms"`

`=6t^2-t-15`