To simplify the expression $-2(p + 4)^2 - 3 + 5p$ into standard form, follow these steps:

Step 1: Expand the squared term

First, expand $(p + 4)^2$: $(p + 4)^2 = p^2 + 8p + 16$ Now, substitute this back into the expression: $-2(p^2 + 8p + 16) - 3 + 5p$

Step 2: Distribute the $-2$ across the expanded expression

$-2 \times p^2 - 2 \times 8p - 2 \times 16 = -2p^2 - 16p - 32$ So the expression now is: $-2p^2 - 16p - 32 - 3 + 5p$

Step 3: Combine like terms

Combine the $p$ terms: $-16p + 5p = -11p$ Now, combine the constant terms: $-32 - 3 = -35$

Step 4: Write the final expression in standard form

The expression in standard form is: $-2p^2 - 11p - 35$

So, the simplified expression is $-2p^2 - 11p - 35$.

Do you have any questions or need more details on any step?

Here are 5 related questions for further practice:

1. Simplify $3(p - 2)^2 + 4p - 5$.
2. Expand and simplify $-4(p + 3)^2 + 7p + 9$.
3. Simplify $2(p^2 + 3p + 4) - 5p + 8$.
4. How do you combine like terms in the expression $-6p^2 + 3p - 2p^2 + 5$?
5. Simplify and write in standard form: $-3(p - 1)^2 + 2p - 4$.

Tip: When simplifying expressions, always expand the terms first and then combine like terms to ensure the expression is in its simplest form.