Which expression is a factor of $$ 16 p^{2}-64 $$ ash Number 5 4p-64 4p-2 $$ 8 p-8 $$ $$ 8 p-32 $$

Question

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To determine which expression is a factor of $$ 16p^2 - 64 $$, let's factor the polynomial step-by-step.

### Step 1: Recognize the Difference of Squares

The expression $$ 16p^2 - 64 $$ is a difference of squares since:
$$ 16p^2 = (4p)^2 $$
$$ 64 = 8^2 $$

### Step 2: Apply the Difference of Squares Formula

The difference of squares formula is:
$$ a^2 - b^2 = (a - b)(a + b) $$

Applying this to $$ 16p^2 - 64 $$:
$$ 16p^2 - 64 = (4p)^2 - 8^2 = (4p - 8)(4p + 8) $$

### Step 3: Simplify the Factors

You can factor out common factors from each binomial:
$$ 4p - 8 = 4(p - 2) $$
$$ 4p + 8 = 4(p + 2) $$

So, the complete factorization is:
$$ 16p^2 - 64 = 16(p - 2)(p + 2) $$

### Step 4: Compare with Given Options

The factored form $$ 16(p - 2)(p + 2) $$ indicates that the linear factors are $$ (p - 2) $$ and $$ (p + 2) $$. However, the provided options are:

1. $$ 4p - 64 $$
2. $$ 4p - 2 $$
3. $$ 8p - 8 $$
4. $$ 8p - 32 $$

None of these directly match $$ p - 2 $$ or $$ p + 2 $$. However, if we consider multiples or simplified forms:

- $$ 8p - 8 = 8(p - 1) $$ does not correspond to $$ p - 2 $$ or $$ p + 2 $$.
- $$ 8p - 32 = 8(p - 4) $$ also does not correspond.

### Conclusion

None of the provided options are exact factors of $$ 16p^2 - 64 $$. The correct linear factors should be $$ p - 2 $$ and $$ p + 2 $$. If forced to choose the closest option based on the factorization process, **$$ 8p - 8 $$** might be considered, but it's not an exact factor.

**Final Answer:** None of the given expressions is an exact factor of $$ 16p^2 - 64 $$.
None of the given expressions is an exact factor of $$ 16p^2 - 64 $$.

Which expression is a factor of \( 16 p^{2}-64 \) ash Number 5 4p-64 4p-2 \( 8 p-8 \) \( 8 p-32 \)

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