how do you do anarrays and an expanded algorithm problem find each partial product then add to find the product.

29
x47
--------
()()
()()()
()()()
+ ()()()
--------
()()()()

To solve this problem using an expanded algorithm, follow these steps:

1. Create a grid with the number of rows equal to the number of digits in the second number (47 in this case), and the number of columns equal to the number of digits in the first number (29 in this case). In this example, we need a grid with 2 rows and 2 columns.

```
29
x47
```

2. Starting from the rightmost digit of the second number (7 in this case), multiply it with each digit in the first number. Write the partial products below the line.

```
29
x47
--------
63 <-- 7 x 9
+ 140 <-- 7 x 2
--------
```

3. Repeat step 2 for the second digit of the second number (4 in this case).

```
29
x47
--------
63 <-- 7 x 9
+ 140 <-- 7 x 2
--------
116 <-- 4 x 9
+ 280 <-- 4 x 2
--------
```

4. Add up all the partial products to find the final product. Write the sum below the line.

```
29
x47
--------
63 <-- 7 x 9
+ 140 <-- 7 x 2
--------
116 <-- 4 x 9
+ 280 <-- 4 x 2
--------
1363
```

So, the product of 29 and 47 is 1363.

By breaking down the multiplication into partial products and then adding them up, the expanded algorithm simplifies the multiplication process and makes it easier to understand.