If $$ C=2 x^{2}+5 x-1 $$ and $$ D=x-1 $$, find an expression that equals $$ C-3 D $$ in standard form. Answer Attempt 1 out of 2

Question

UpStudy AI · Accepted Answer

To find an expression that equals $$ C - 3D $$ in standard form, follow these steps:

Given:
- $$ C = 2x^{2} + 5x - 1 $$
- $$ D = x - 1 $$

**Step 1: Multiply $$ D $$ by 3**

$$
3D = 3(x - 1) = 3x - 3
$$

**Step 2: Subtract $$ 3D $$ from $$ C $$**

$$
C - 3D = (2x^{2} + 5x - 1) - (3x - 3)
$$

**Step 3: Distribute the negative sign**

$$
C - 3D = 2x^{2} + 5x - 1 - 3x + 3
$$

**Step 4: Combine like terms**

$$
\begin{align*}
2x^{2} &+ 5x - 3x \
&+ (-1 + 3) \
= 2x^{2} &+ 2x + 2
\end{align*}
$$

**Final Expression in Standard Form:**

$$
C - 3D = 2x^{2} + 2x + 2
$$

This is the simplified expression in standard form.
$$ C - 3D = 2x^{2} + 2x + 2 $$

If \( C=2 x^{2}+5 x-1 \) and \( D=x-1 \), find an expression that equals \( C-3 D \) in standard form. Answer Attempt 1 out of 2