Question 6 of 8, Step 1 of 1 Completely factor the expression by grouping, if possible. $$ s+c u+s x+u x $$ Answer How to enter your answer (opens in new window)

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UpStudy AI · Accepted Answer

To factor the expression $$ s + cu + sx + ux $$ by grouping, we can follow these steps:

1. **Group the terms**: We can group the terms in pairs. Let's group the first two terms and the last two terms:
   $$
   (s + cu) + (sx + ux)
   $$

2. **Factor out the common factors in each group**:
   - In the first group $$ s + cu $$, there is no common factor to factor out.
   - In the second group $$ sx + ux $$, we can factor out $$ x $$:
   $$
   (s + cu) + x(s + u)
   $$

3. **Combine the groups**: Now we can see that both groups contain a common factor of $$ s + u $$:
   $$
   s + cu + x(s + u) = (s + u)(1 + x) + cu
   $$

4. **Final expression**: The expression can be factored as:
   $$
   (s + u)(1 + x) + cu
   $$

However, we can also check if we can factor it further. Let's rewrite the expression:
$$
s + cu + sx + ux = s(1 + x) + u(c + x)
$$

Now we can see that we can factor it as:
$$
(s + u)(1 + x)
$$

Thus, the completely factored form of the expression $$ s + cu + sx + ux $$ is:
$$
(s + u)(1 + x)
$$

This is the final answer.
The expression $$ s + cu + sx + ux $$ can be factored as $$ (s + u)(1 + x) $$.

Question 6 of 8, Step 1 of 1 Completely factor the expression by grouping, if possible. \[ s+c u+s x+u x \] Answer How to enter your answer (opens in new window)

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