Question

w.11 multiply polynomials 58a
find the product. simplify your answer.
$(2p - 4)(p^{2} - p + 4)$

Explanation:

Step1: Distribute $2p$ to each term

$2p \cdot p^2 + 2p \cdot (-p) + 2p \cdot 4$
$= 2p^3 - 2p^2 + 8p$

Step2: Distribute $-4$ to each term

$-4 \cdot p^2 + (-4) \cdot (-p) + (-4) \cdot 4$
$= -4p^2 + 4p - 16$

Step3: Combine all terms

$2p^3 - 2p^2 + 8p - 4p^2 + 4p - 16$

Step4: Combine like terms

$2p^3 + (-2p^2 -4p^2) + (8p +4p) -16$
$= 2p^3 -6p^2 +12p -16$

Answer:

$2p^3 -6p^2 +12p -16$