Final answer:
To solve for the expression 2c + 2d²c - 2d in standard form, we first find c by rearranging the equation c = r - 8c to get c = r/9, and then substitute this and the expression for d into the given equation. Subsequent simplification is required to reach the standard form.
Step-by-step explanation:
To find an expression that equals 2c + 2d²c - 2d in standard form, we first need the expressions for c and d given as c = r - 8c and d = -r² + 8r + 7.
We begin by solving the equation for c to express it in terms of r.
Starting with c = r - 8c, we can rearrange the terms to find c:
Add 8c to both sides: 9c = rDivide by 9: c = r/9
Now we substitute this expression for c into the given equation 2c + 2d²c - 2d, replace d with its given expression, and simplify.
This process might involve further algebraic manipulation, including expanding and combining like terms to reach the standard form.
Due to the complexity of the equation and the possibility of making errors, it is recommended to thoroughly check each step and verify the calculations manually or with the aid of a calculator.