Question

simplify the expression $-2(p + 4)^2 - 3 + 5p$. what is the simplified expression in standard form?
$\bigcirc\\ -2p^2 - 11p - 35$
$\bigcirc\\ 2p^2 + 21p + 29$
$\bigcirc\\ -2p^2 + 13p + 13$
$\bigcirc\\ 4p^2 + 37p - 67$

Explanation:

Step1: Expand \((p + 4)^2\)

Using the formula \((a + b)^2 = a^2 + 2ab + b^2\), where \(a = p\) and \(b = 4\), we get \((p + 4)^2 = p^2 + 8p + 16\).

Step2: Multiply by -2

Multiply the expanded form by -2: \(-2(p^2 + 8p + 16) = -2p^2 - 16p - 32\).

Step3: Combine like terms

Now, combine with the remaining terms \(-3 + 5p\):

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Answer:

-2p² - 11p - 35 (corresponding to the first option)