Question

How to Multiply Binomials Vertically.
Step 1: Make sure both binomials are written in
1 Answer I-----.
order.
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• Step 2: Set up the problem
i Answer
,, with factors aligned by like terms.
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• Step 3: Multiply each term of the top binomial by the last term of the
• Answer 1-----:
binomial.
• Step 4: Multiply each term of the i Answer ____.
binomial by the first term of the bottom binomial.
・ Step 5：
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' the two smaller products (partial products).
• Step 6: Simplify your answer.
# Add
#top
# bottom
# vertically
# descending

Answer 1

To multiply binomials vertically using the steps you outlined, let's break down the process in a clear manner:

### Example Problem:
Let's take the binomials \( (a + b) \) and \( (c + d) \) to illustrate the steps.

### Step 1: Write the Binomials in Order
Make sure both binomials are positioned appropriately:
```
a + b
× c + d
```

### Step 2: Set Up the Problem
Align the binomials in a column, ensuring like terms are lined up:
```
a b
× c d
```

### Step 3: Multiply Each Term of the Top Binomial by the Last Term of the Bottom Binomial
Multiply the first term of the top binomial by each term of the bottom binomial.
```
a b
× c d
---------------
ad (multiply b by d)
```

### Step 4: Multiply Each Term of the Binomial by the First Term of the Bottom Binomial
Next, multiply the second term of the top binomial by each term of the bottom binomial.
```
a b
× c d
---------------
ad (multiply b by d)
+ ac (multiply a by c)
---------------
```

### Step 5: Add the Two Smaller Products (Partial Products)
Now, add the products obtained from Step 3 and Step 4:
```
a b
× c d
---------------
ad
+ ac
---------------
ac + bd (Combine like terms if there are any)
```

### Step 6: Simplify Your Answer
The final answer after simplification might be:
```
ac + bd
```

### Example Calculation:
Assume you want to multiply \( (2 + 3) \) by \( (4 + 5) \).

1. Set it up:
```
2 3
× 4 5
```
2. Multiply:
- \( 3 \times 5 = 15 \)
- \( 2 \times 5 = 10 \)
- \( 3 \times 4 = 12 \)
- \( 2 \times 4 = 8 \)

3. Add:
- The partial products: \( 10 + 15 + 12 + 8 = 45 \)

After applying the above systematic method to multiplying binomials vertically, your answer is:
```
45
```

This method ensures that you keep your work organized and reduces the chance of errors during the multiplication process.