Final answer:
The simplified expression is 2m² + mn + 5. Substituting m=-2 and n=1, the value of the expression is 11.
Step-by-step explanation:
The expression given is 2(m²+mn)+5-mn. First, we'll simplify the expression by distributing the 2 into the terms within the parenthesis and then combining like terms.
- Distribute the 2: 2 × m² + 2 × mn + 5 - mn
- Simplify: 2m² + 2mn + 5 - mn
- Combine like terms: 2m² + (2mn - mn) + 5
- Further simplify: 2m² + mn + 5
To find the value when m = -2 and n = 1:
- Substitute m and n into the expression: 2(-2)² + (-2)(1) + 5
- Calculate the square: 2(4) - 2 + 5
- Multiply and combine terms: 8 - 2 + 5
- Final value: 11