Let's simplify the given expression step by step:
Given expression:
[tex]\[ -m - n + x(m + n) \][/tex]
1. Start by distributing [tex]\( x \)[/tex] through the parentheses:
[tex]\[ -m - n + x(m) + x(n) \][/tex]
2. This simplifies to:
[tex]\[ -m - n + xm + xn \][/tex]
3. Next, group the like terms together:
[tex]\[ (-m + xm) + (-n + xn) \][/tex]
4. Factor out the common terms [tex]\( m \)[/tex] and [tex]\( n \)[/tex]:
[tex]\[ m(-1 + x) + n(-1 + x) \][/tex]
5. Notice that both terms have a common factor, [tex]\((-1 + x)\)[/tex]:
[tex]\[ (-1 + x)(m + n) \][/tex]
So the simplified form of the expression [tex]\(-m - n + x(m + n)\)[/tex] is:
[tex]\[ (-1 + x)(m + n) \][/tex]
