Question

How do you simplify `-1/4m(8m^2+m-7)`?

Answer 1

See a solution process below:

Explanation:

To simplify this expression multiply each term within the parenthesis by the term outside the parenthesis:

`color(red)(-1/4m)(8m^2 + m - 7) =>`

`(color(red)(-1/4m) * 8m^2) + (color(red)(-1/4m) * m) - (color(red)(-1/4m) * 7) =>`

`-8/4m^3 + (-1/4m^2) - (-7/4m) =>`

`-2m^3 - 1/4m^2 + 7/4m`

Answer 2

`- (m/4)(m + 1)(8m - 7)`

Explanation:

`f(m) = - (m/4)(8m^2 + m - 7)`
Factor the trinomial in parentheses:
`y = 8m^2 + m - 7`
Since a - b + c = 0, use shortcut. The two real roots are - 1 and
`-c/a = 7/8`. The 2 factors are: (m + 1) and `(m - 7/8)`.
Factored form of y is:
`y = 8(m + 1)(m - 7/8) = (m + 1)(8m - 7)`
Finally,
`f(m) = - (my)/4 = - (m/4)(m + 1)(8m - 7)`