Question If $$ C=2 m^{2}+m $$ and $$ D=2-6 m+2 m^{2} $$, find an expression that equals $$ 2 C-2 D $$ in standard form.

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

**Given:**
$$
C = 2m^{2} + m
$$
$$
D = 2 - 6m + 2m^{2}
$$

**Step 1: Calculate $$ 2C $$**
$$
2C = 2 \times (2m^{2} + m) = 4m^{2} + 2m
$$

**Step 2: Calculate $$ 2D $$**
$$
2D = 2 \times (2 - 6m + 2m^{2}) = 4 - 12m + 4m^{2}
$$

**Step 3: Subtract $$ 2D $$ from $$ 2C $$**
$$
2C - 2D = (4m^{2} + 2m) - (4 - 12m + 4m^{2})
$$

**Step 4: Distribute the negative sign and combine like terms**
$$
2C - 2D = 4m^{2} + 2m - 4 + 12m - 4m^{2}
$$
$$
2C - 2D = (4m^{2} - 4m^{2}) + (2m + 12m) - 4
$$
$$
2C - 2D = 0m^{2} + 14m - 4
$$
$$
2C - 2D = 14m - 4
$$

**Final Answer:**
$$
2C - 2D = 14m - 4
$$
$$ 2C - 2D = 14m - 4 $$

Question If \( C=2 m^{2}+m \) and \( D=2-6 m+2 m^{2} \), find an expression that equals \( 2 C-2 D \) in standard form.

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