Simplify the following :
(i) `(-7)xx(-5)+6xx(-3)-(-9)xx8`
(ii) `(-6)xx(-11)xx0-5xx(-12)+(-16)xx4`.

Options

A. `(i) 88`
`(ii) -8`
B. `(i) 89`
`(ii) -4`
C. `(i) 89`
`(ii) 4`
D. `(i) 79`
`(ii) -14`

Answer

Let's simplify the given expressions step by step.

### Part (i): Simplify `(-7)xx(-5) + 6xx(-3) - (-9)xx8`

**Step 1: Identify the operations**
We have three terms to simplify: `(-7)xx(-5)`, `6xx(-3)`, and `-(-9)xx8`.

**Step 2: Simplify each term**
- For `(-7)xx(-5)`:
- Negative times negative equals positive.
- Calculation: `7 * 5 = 35`
- Result: `(-7)xx(-5) = 35`

- For `6xx(-3)`:
- Positive times negative equals negative.
- Calculation: `6 * 3 = 18`
- Result: `6xx(-3) = -18`

- For `-(-9)xx8`:
- Negative times positive equals negative, but we have a negative outside which turns it positive.
- Calculation: `9 * 8 = 72`
- Result: `-(-9)xx8 = 72`

**Step 3: Combine the results**
Now we combine the results from the three terms:
\[ 35 + (-18) + 72 \]

**Step 4: Perform the addition**
- First, calculate \( 35 - 18 = 17 \)
- Then, add \( 17 + 72 = 89 \)

**Final Result for Part (i):**
\[ 89 \]

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### Part (ii): Simplify `(-6)xx(-11)xx0 - 5xx(-12) + (-16)xx4`

**Step 1: Identify the operations**
We have three terms to simplify: `(-6)xx(-11)xx0`, `-5xx(-12)`, and `(-16)xx4`.

**Step 2: Simplify each term**
- For `(-6)xx(-11)xx0`:
- Any number multiplied by zero equals zero.
- Result: `(-6)xx(-11)xx0 = 0`

- For `-5xx(-12)`:
- Negative times negative equals positive.
- Calculation: `5 * 12 = 60`
- Result: `-5xx(-12) = 60`

- For `(-16)xx4`:
- Negative times positive equals negative.
- Calculation: `16 * 4 = 64`
- Result: `(-16)xx4 = -64`

**Step 3: Combine the results**
Now we combine the results from the three terms:
\[ 0 + 60 - 64 \]

**Step 4: Perform the addition**
- First, calculate \( 0 + 60 = 60 \)
- Then, subtract \( 60 - 64 = -4 \)

**Final Result for Part (ii):**
\[ -4 \]

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