Intermediate Algebra, Chapter 5, 5.2, Section 5.2, Problem 35

Combine the like terms of the polynomial $-m^3 + 2m^3 + 6m^3$

According to the distributive property, for any numbers $a, b,$ and $c, a(b+c)=ab+ac$ and $(b+c)a=ba+ca$. Here, $m^3$ is a factor of both $-m^3$ and $2m^3$
$(-1 + 2)m^3 + 6m^3$

To add integers with different signs, subtract their absolute values and give the result the same sign as the integer with the greater absolute value.
In this example, subtract the absolute values of $-1$ and $2$ and give the result the same sign as the integer with the greater absolute value.
$(1) m^3 + 6m^3$

Remove the parentheses.
$m^3 + 6m^3$

Again, according to the distributive property, for any numbers $a, b,$ and $c, a(b+c)=ab+ac$ and $(b+c)a=ba+ca$. Here, $m^3$ is a factor of both $m^3$ and $6m^3$
$(1 + 6)m^3$

Add 6 to 1 to get 7.
$(7)m^3$

Remove the parenthesis
Thus, the answer is $7m^3$