Question Uf $$ C=r-8 $$ and $$ D=-r^{2}+8 r+7 $$, find an expression that equals $$ 2 C+2 D $$ in standard form

Question

UpStudy AI · Accepted Answer

To find an expression for $$ 2C + 2D $$ in standard form, follow these steps:

Given:
$$
C = r - 8
$$
$$
D = -r^2 + 8r + 7
$$

Calculate $$ 2C + 2D $$:
$$
2C + 2D = 2(r - 8) + 2(-r^2 + 8r + 7)
$$

Distribute the 2:
$$
= 2r - 16 + (-2r^2 + 16r + 14)
$$

Combine like terms:
$$
= -2r^2 + (2r + 16r) + (-16 + 14)
$$
$$
= -2r^2 + 18r - 2
$$

So, the expression in standard form is:
$$
-2r^2 + 18r - 2
$$

**Answer:**  
After simplifying, an equivalent expression is –2 r² + 18 r – 2
$$ 2C + 2D = -2r^2 + 18r - 2 $$

Question Uf \( C=r-8 \) and \( D=-r^{2}+8 r+7 \), find an expression that equals \( 2 C+2 D \) in standard form