5. Which of the following shows 15 abc expanded correctly? 5* abc $$ 3 * 5 $$ * $$ a * b $$ * $$ c $$ $$ 15(a+b+c) $$ abc15

Question

UpStudy AI · Accepted Answer

The correct expansion of $$15abc$$ breaks down the coefficient $$15$$ into its prime factors and maintains the product with the variables $$a$$, $$b$$, and $$c$$. Let's evaluate each option:

1. **$$5 \times abc$$**
   - This represents $$5abc$$, which is not equal to $$15abc$$.

2. **$$(3 \times 5) \times (a \times b \times c)$$**
   - This correctly breaks down $$15$$ into $$3 \times 5$$ and maintains the multiplication with $$a$$, $$b$$, and $$c$$. 
   - Hence, it accurately represents $$15abc$$.

3. **$$15(a + b + c)$$**
   - This expression distributes $$15$$ over the sum $$a + b + c$$, resulting in $$15a + 15b + 15c$$, which is not equivalent to $$15abc$$.

4. **$$abc15$$**
   - While this can represent $$15abc$$, it doesn't show the expansion or factorization of the coefficient $$15$$.

**Therefore, the correct expansion is:**

$$
(3 \times 5) \times (a \times b \times c)
$$

**Answer:**  
$$(3 \times 5)\times(a \times b) \times c$$
The correct expansion of $$15abc$$ is $$(3 \times 5) \times (a \times b \times c)$$.

5. Which of the following shows 15 abc expanded correctly? 5* abc \( 3 * 5 \) * \( a * b \) * \( c \) \( 15(a+b+c) \) abc15

Real Tutor Solution

Answer

Solution

The Deep Dive

Related Questions

Latest Algebra Questions