Question

How do you simplify `f( x ) = 2( 4x - 5) + 4( 4x + 14)`?

Answer 1

See a solution process below:

Explanation:

First, expand the terms within parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis:

`f(x) = color(red)(2)(4x - 5) + color(blue)(4)(4x + 14)`

`f(x) = (color(red)(2) xx 4x) - (color(red)(2) xx 5) + (color(blue)(4) xx 4x) + (color(blue)(4) xx 14)`

`f(x) = 8x - 10 + 16x + 56`

Next, group like terms on the right side of the function:

`f(x) = 8x + 16x - 10 + 56`

Now, combine like terms:

`f(x) = (8 + 16)x + (-10 + 56)`

`f(x) = 24x + 46`

Answer 2

`f(x)=color(green)(24x+46)`

Explanation:

Using the distributive law:
`color(white)("XXX")2(4x-5) =2xx4x -2xx5`
`color(white)("XXXXXXXXX")=8x-10`
and
`color(white)("XXX")4(4x+14)=4xx4x+4xx14`
`color(white)("XXXXXXXXX")=16x+56`

So,
`color(white)("XXX")2(4x-5)+4(4x+14)`
`color(white)("XXXXXXXXX")=8x-10+16x+56`

then combining like terms
`color(white)("XXXXXXXXX")=8x+16x-10+56`

`color(white)("XXXXXXXXX")=24x+46`