# 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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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)

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

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