Final answer:
The expression 10w - 7 - 1 - 5w² + 12w simplifies to 22w - 8 - 5w² after combining like terms and performing the arithmetic operations accordingly.
Step-by-step explanation:
The student's question involves adding, subtracting, and/or multiplying monomials. First, we need to combine like terms and then perform the operations. Looking at the expression 10w - 7 - 1 - 5w² + 12w, we notice that the terms 10w and 12w can be combined (as they are like terms), as well as the constants -7 and -1:
Step 1: Combine like terms.
(10w + 12w) - (7 + 1) - 5w²
Step 2: Simplify the expression by performing addition and subtraction.
22w - 8 - 5w²
The expression is now simplified, and all like terms have been combined. The coefficient signs and arithmetic operations were handled according to rules of operations with positive and negative numbers. Multiplication between monomials follows the principle of adding exponents when the bases are the same, but in this case, there was no need for multiplication.