Find the products, using distributive laws: (i) `740xx105`
(ii)`245xx1008`
(iii)`947xx96`
(iv)`996xx367`
(v) `472xx1097`
(vi) `580xx64`
(vii)`439xx997`
(viii) `1553xx198`

Answer

To solve the given problems using the distributive law, we will break down each multiplication into simpler parts. Let's go through each part step by step.

### (i) \(740 \times 105\)

1. **Break down 105**:
\[ 740 \times 105 = 740 \times (100 + 5) \]

2. **Apply the distributive law**:
\[ = 740 \times 100 + 740 \times 5 \]

3. **Calculate each part**:
\[ 740 \times 100 = 74000 \]
\[ 740 \times 5 = 3700 \]

4. **Add the results**:
\[ 74000 + 3700 = 77700 \]

**Final Answer**: \(740 \times 105 = 77700\)

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### (ii) \(245 \times 1008\)

1. **Break down 1008**:
\[ 245 \times 1008 = 245 \times (1000 + 8) \]

2. **Apply the distributive law**:
\[ = 245 \times 1000 + 245 \times 8 \]

3. **Calculate each part**:
\[ 245 \times 1000 = 245000 \]
\[ 245 \times 8 = 1960 \]

4. **Add the results**:
\[ 245000 + 1960 = 246960 \]

**Final Answer**: \(245 \times 1008 = 246960\)

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### (iii) \(947 \times 96\)

1. **Break down 96**:
\[ 947 \times 96 = 947 \times (100 - 4) \]

2. **Apply the distributive law**:
\[ = 947 \times 100 - 947 \times 4 \]

3. **Calculate each part**:
\[ 947 \times 100 = 94700 \]
\[ 947 \times 4 = 3788 \]

4. **Subtract the results**:
\[ 94700 - 3788 = 90912 \]

**Final Answer**: \(947 \times 96 = 90912\)

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### (iv) \(996 \times 367\)

1. **Break down 367**:
\[ 996 \times 367 = 996 \times (300 + 67) \]

2. **Apply the distributive law**:
\[ = 996 \times 300 + 996 \times 67 \]

3. **Calculate each part**:
\[ 996 \times 300 = 298800 \]
\[ 996 \times 67 = 66732 \]

4. **Add the results**:
\[ 298800 + 66732 = 365532 \]

**Final Answer**: \(996 \times 367 = 365532\)

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### (v) \(472 \times 1097\)

1. **Break down 1097**:
\[ 472 \times 1097 = 472 \times (1000 + 97) \]

2. **Apply the distributive law**:
\[ = 472 \times 1000 + 472 \times 97 \]

3. **Calculate each part**:
\[ 472 \times 1000 = 472000 \]
\[ 472 \times 97 = 45864 \]

4. **Add the results**:
\[ 472000 + 45864 = 517864 \]

**Final Answer**: \(472 \times 1097 = 517864\)

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### (vi) \(580 \times 64\)

1. **Break down 64**:
\[ 580 \times 64 = 580 \times (60 + 4) \]

2. **Apply the distributive law**:
\[ = 580 \times 60 + 580 \times 4 \]

3. **Calculate each part**:
\[ 580 \times 60 = 34800 \]
\[ 580 \times 4 = 2320 \]

4. **Add the results**:
\[ 34800 + 2320 = 37120 \]

**Final Answer**: \(580 \times 64 = 37120\)

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### (vii) \(439 \times 997\)

1. **Break down 997**:
\[ 439 \times 997 = 439 \times (1000 - 3) \]

2. **Apply the distributive law**:
\[ = 439 \times 1000 - 439 \times 3 \]

3. **Calculate each part**:
\[ 439 \times 1000 = 439000 \]
\[ 439 \times 3 = 1317 \]

4. **Subtract the results**:
\[ 439000 - 1317 = 437683 \]

**Final Answer**: \(439 \times 997 = 437683\)

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### (viii) \(1553 \times 198\)

1. **Break down 198**:
\[ 1553 \times 198 = 1553 \times (200 - 2) \]

2. **Apply the distributive law**:
\[ = 1553 \times 200 - 1553 \times 2 \]

3. **Calculate each part**:
\[ 1553 \times 200 = 310600 \]
\[ 1553 \times 2 = 3106 \]

4. **Subtract the results**:
\[ 310600 - 3106 = 307494 \]

**Final Answer**: \(1553 \times 198 = 307494\)

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