Fill in the blanks.

1. [tex]13 \times (26 + 45) = 13 \times 26 + 13 \times 45[/tex]

2. [tex](57 + 82) \times 64 = (57 \times 64) + (82 \times 64)[/tex]

3. [tex]93 \times 102 = 93 \times (100 + 2) = 93 \times 100 + 93 \times 2[/tex]

4. [tex]\ \textless \ br/\ \textgreater \ \begin{aligned}\ \textless \ br/\ \textgreater \ 99 \times 76 & = (100 - 1) \times 76 \\\ \textless \ br/\ \textgreater \ & = (100 \times 76) - (1 \times 76) \\\ \textless \ br/\ \textgreater \ & = 7600 - 76 \\\ \textless \ br/\ \textgreater \ & = 7524\ \textless \ br/\ \textgreater \ \end{aligned}\ \textless \ br/\ \textgreater \ [/tex]

5. [tex]\ \textless \ br/\ \textgreater \ \begin{aligned}\ \textless \ br/\ \textgreater \ 112 \times 998 & = 112 \times (1000 - 2) \\\ \textless \ br/\ \textgreater \ & = (112 \times 1000) - (112 \times 2) \\\ \textless \ br/\ \textgreater \ & = 112000 - 224 \\\ \textless \ br/\ \textgreater \ & = 111776\ \textless \ br/\ \textgreater \ \end{aligned}\ \textless \ br/\ \textgreater \ [/tex]

Let's carefully fill in the blanks step-by-step for each section.

### 1) [tex]$ 13 \times (26 + 45) = $[/tex]
- Expression: [tex]$ 13 \times (26 + 45) $[/tex]
- [tex]$ \quad (13 \times 26) + (13 \times 45) $[/tex]
- We have: [tex]$ x26 + 13 \times \square ) $[/tex]
- Thus, [tex]$ 13 \times (26 + 45) = (13 \times 26) + (13 \times 45) $[/tex]

### 2) [tex]$ (57 + 82) \times 64 = $[/tex]
- Expression: [tex]$ (57 + 82) \times 64 $[/tex]
- [tex]$ \quad (57 \times 64 ) + ( 82 \times 64) $[/tex]
- Fill in: [tex]$ (57 \times \quad \square ) + ( \square \times 64) $[/tex]
- Thus, [tex]$ (57 + 82) \times 64 = (57 \times 64) + (82 \times 64) $[/tex]

### 3) [tex]$ 93 \times 102 = $[/tex]
- Expression: [tex]$ 93 \times 102 $[/tex]
- [tex]$ \quad 93 \times (100 + 2) $[/tex]
- Fill in: [tex]$ \quad 93 \times (100 + \square) $[/tex]
- That implies, [tex]$ \quad 93 \times (100 + 2) $[/tex]
- Breaking down: [tex]$ 93 \times 100 + 93 \times 2 $[/tex]
- Thus, [tex]$ 93 \times 102 = 93 \times 100 + 93 \times 2 $[/tex]

### 4) [tex]$ 99 \times 76 = $[/tex]
- Expression: [tex]$ 99 \times 76 $[/tex]
- [tex]$ (100 - 1) \times 76 $[/tex]
- Fill in: [tex]$ \quad (100 - \square) \times 76 $[/tex]
- That should be: [tex]$ \quad (100 - 1) \times 76 $[/tex]
- Breaking down: [tex]$ 100 \times 76 - 1 \times 76 $[/tex]
- Thus, [tex]$ 99 \times 76 = (100 \times 76) - (1 \times 76) $[/tex]

### 5) [tex]$ 112 \times 998 = $[/tex]
- Expression: [tex]$ 112 \times 998 $[/tex]
- Breaking down: [tex]$ 112 \times (1000 - 2) $[/tex]
- Fill in: [tex]$ 112 \times (\ldots - \square) $[/tex]
- Completing: [tex]$ 112 \times (1000 - 2) $[/tex]
- Expanding: [tex]$ (112 \times 1000) - (112 \times 2) $[/tex]
- Thus:
[tex]\[ \begin{aligned} 112 \times 998 &= 112 \times (1000 - 2) \\ &= (112 \times 1000) - (112 \times 2) \\ &= 111776 \end{aligned} \][/tex]

### Summary of the steps:

1. [tex]$ 13 \times (26 + 45) = (13 \times 26) + (13 \times 45) $[/tex]

2. [tex]$ (57 + 82) \times 64 = (57 \times 64) + (82 \times 64) $[/tex]

3. [tex]$ 93 \times 102 = 93 \times (100 + 2) = 93 \times 100 + 93 \times 2 = 94 + 189 $[/tex]

4. [tex]$ 99 \times 76 = (100 - 1) \times 76 = (100 \times 76) - (1 \times 76) $[/tex]

5. [tex]$ 112 \times 998 = 112 \times (1000 - 2) = (112 \times 1000) - (112 \times 2) = 111776 $[/tex]