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

2 Answers
smendyka
Jul 19, 2017

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#

Nghi N
Jul 19, 2017

#- (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)#

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