Simplify the following expression by removing the grouping symbols and collecting like terms.m-(m+1)+(m-3)-(4m^2+6m+4)

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neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

To simplify m-(m+1)+(m-3)-(4m^2+6m+4):

Solution:

First there is m..................................(1)Then

-(m+1) which is equal to -m-1................................(2) Then

+(m-3) which is equal to m-3..................................(3) Then

-(4m^2+6m+4) which is equal to -4m^2-6m-4...........(4)

Adding the expressions at (1) to (4), we get:

m -m-1+m-3-4m^2-6m-4

Collecting like terms (m^2 first  and then m's and then numbers) together, we get:

-4m^2+m-m+m-6m-1-3-4

=-4m^2-5m-8 or

=-(4m^2+5m+8)

krishna-agrawala's profile pic

krishna-agrawala | College Teacher | (Level 3) Valedictorian

Posted on

The rules for simplifying an expression of the type given in the question by removing grouping symbols, i.e. parenthesis, are simple. When the parenthesis is preceded by a positive sign, all the term within the parenthesis retain their original signs after removing parenthesis. When the parenthesis is preceded by a negative sign, all the term within the parenthesis have their original signs reversed after removing parenthesis, that a positive sign is changed to negative and a negative sign is changed to positive. Please not that when no sign is explicitly indicated before a term it means a term with positive value.

Using this rule we simplify the given expression as follows.

E = m - (m + 1) + (m-3) - (4m^2 + 6m + 4)

= m - m - 1 +  m - 3 - 4m^2 - 6m - 4

= - 4m^2 + m - m + m - 6m - 1 - 3 - 4

= - 4m^2 + 2m - 7m - 8

= - 4m^2 - 5m - 8

jilllenz's profile pic

jilllenz | High School Teacher | eNotes Newbie

Posted on

You must use the distributive property to remove grouping symbols.  To use the distributive property:  multiply everything inside the grouping symbols by the number that is in front (or behind) the grouping symbols.  In this problem 2 sets of parantheses (grouping sysmbols) have a subtraction sign in front so you would multiply by -1.

m-(m+1)+m-3)-(4m^2+6m+4) could be rewritten as follows:

1m + -1(m+1) + 1(m - 3) + -1(4m^2 + 6m + 4)

1m  + -1m + -1 + 1m + -3 + -4m^2 + -6m + -4

combine like terms:

-4m^2 + -5m + -8

this could also be written:

-4m^2 - 5m - 8

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