Question

How do you multiply `(4n - 1) ( 3n + 4)`?

Answer 1

`12n^2+13n-4`

Explanation:

start off by writing out
`(4n-1)(3n+4)`

multiply by distributing
`(4n)(3n)=12n²`
`(4n)(4)=16n`

so far you have
`12n² +16n`

now distribute again but with the -1
`(-1)(3n)=-3n`
`(-1)(4)=-4`

you now have `12n^2 + 16n-3n-4`

subtract like terms
`(16n-3n)=13n`

put it together and you have:
`12n^2+13n-4`

Answer 2

Use FOIL to find:

`(4n-1)(3n+4) = 12n^2+13n-4`

Explanation:

If you find it helpful, you can use the FOIL ("First", "Outside", "Inside", "Last") mnemonic to help to combine all the required terms:

`(4n-1)(3n+4) = overbrace((4n*3n))^"First"+overbrace((4n*4))^"Outside"+overbrace(((-1)*3n))^"Inside"+overbrace(((-1)*4))^"Last"`

`color(white)((4n-1)(3n+4)) = 12n^2+16n-3n-4`

`color(white)((4n-1)(3n+4)) = 12n^2+13n-4`

FOIL can be used when multiplying any two binomials.