Question

How do you simplify the product `(6x - 5)(3x + 1)` and write it in standard form?

Answer 1

`18x^2-9x-5`

Explanation:

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

`=(color(red)(6x-5))(3x+1)`

`=color(red)(6x)(3x+1)color(red)(-5)(3x+1)larrcolor(blue)"distribute"`

`=(color(red)(6x)xx3x)+(color(red)(6x)xx1)+(color(red)(-5)xx3x)+(color(red)(-5)xx1)`

`=18x^2color(blue)(+6x)color(blue)(-15x)-5larrcolor(blue)"collect like terms"`

`=18x^2-9x-5larrcolor(magenta)"in standard form"`

Answer 2

Try using the FOIL method (First, Outside, Inside, Last)
`18x^2-9x-5`

Explanation:

You have to multiply each term in the left bracket by each term in the right bracket. The easiest way to make sure you don't miss anything is to use a systematic method such as FOIL.
The FOIL method means selecting those pairs of numbers to multiply together
Eg. `(a+b)(c+d)=ac+ad+bc+bd`

Question `(6x-5)(3x+1)`
First: `6x*3x=18x^2`
Outside: `6x*1=6x`
Inside:`-5*3x=-15x`
Last: `-5*1=-5`
Now we add them together
`(6x-5)(3x+1)=18x^2+6x+(-15x)+(-5)`
`6x` and `-15x` are like terms so they simplify
leaving us with
`(6x-5)(3x+1)=18x^2-9x-5`