Question

simplify the expression -2(p + 4)² - 3 + 5p. what is the simplified expression in standard form?
-2p² - 11p - 35
2p² + 21p + 29
-2p² + 13p + 13
4p² + 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

\(-2(p^2 + 8p + 16)=-2p^2-16p - 32\).

Step3: Add \(5p - 3\)

\(-2p^2-16p - 32+5p - 3=-2p^2+(-16p + 5p)+(-32 - 3)=-2p^2-11p - 35\).

Answer:

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