Question

How do you simplify `(3+ 2c ) ( 7- 4c )`?

Answer 1

See a solution process below:

Explanation:

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

`(color(red)(3) + color(red)(2c))(color(blue)(7) - color(blue)(4c))` becomes:

`(color(red)(3) xx color(blue)(7)) - (color(red)(3) xx color(blue)(4c)) + (color(red)(2c) xx color(blue)(7)) - (color(red)(2c) xx color(blue)(4c))`

`21 - 12c + 14c - 8c^2`

We can now combine like terms:

`21 + (-12 + 14)c - 8c^2`

`21 + 2c - 8c^2`

Or in standard form:

`-8c^2 + 2c + 21`

Answer 2

`21+2c-8c^2`

Explanation:

`"simplify means to multiply the factors together"`

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

`rArr(color(red)(3+2c))(7-4c)`

`=color(red)(3)(7-4c)color(red)(+2c)(7-4c)`

`"distributing the brackets gives"`

`=(color(red)(3)xx7)+(color(red)(3)xx-4c)+(color(red)(2c)xx7)+(color(red)(2c)xx-4c)`

`=21+(-12c)+14c+(-8c^2)`

`=21+2c-8c^2`