Multiply: $$ (x-2)(2 x-4)(x+6) $$

Question

UpStudy AI · Accepted Answer

To multiply the expression $$(x - 2)(2x - 4)(x + 6)$$, follow these steps:

### Step 1: Multiply the First Two Binomials

First, multiply $$(x - 2)$$ and $$(2x - 4)$$:

$$
\begin{align*}
(x - 2)(2x - 4) &= x \cdot 2x + x \cdot (-4) + (-2) \cdot 2x + (-2) \cdot (-4) \
&= 2x^2 - 4x - 4x + 8 \
&= 2x^2 - 8x + 8
\end{align*}
$$

### Step 2: Multiply the Result by the Third Binomial

Now, multiply the result $$2x^2 - 8x + 8$$ by $$(x + 6)$$:

$$
\begin{align*}
(2x^2 - 8x + 8)(x + 6) &= 2x^2 \cdot x + 2x^2 \cdot 6 + (-8x) \cdot x + (-8x) \cdot 6 + 8 \cdot x + 8 \cdot 6 \
&= 2x^3 + 12x^2 - 8x^2 - 48x + 8x + 48
\end{align*}
$$

### Step 3: Combine Like Terms

Combine the like terms to simplify the expression:

$$
\begin{align*}
2x^3 + (12x^2 - 8x^2) + (-48x + 8x) + 48 &= 2x^3 + 4x^2 - 40x + 48
\end{align*}
$$

### Final Answer

$$
2x^3 + 4x^2 - 40x + 48
$$
The product of $$(x - 2)(2x - 4)(x + 6)$$ is $$2x^3 + 4x^2 - 40x + 48$$.

Multiply:

Upstudy AI Solution

Answer

Solution

The Deep Dive

Related Questions

Latest Algebra Questions