(2p + 3)(p2 – 4p – 7)expand and simplify
(2p + 3)(p² - 4p - 7)2p(p² - 4p - 7) + 3(p² - 4p - 7)Distribute.2p³ - 8p² -14p + 3p² - 12p - 21Combine like terms. (-8p² +3p² makes -5p², and -14p-12p makes -26p)2p³ - 5p² -26p - 21Sometimes it can help to make a table. (see attached)
\((2p+3)(p^2-4p-7)\ \ \ \ |use\ distributive\ property\ a(b\pm c)=ab\pm ac\\\\=(2p)(p^2)-(2p)(4p)-(2p)(7)+(3)(p^2)-(3)(4p)-(3)(7)\\\\use:\ a^n\cdot a^m=a^{n+m}\\and\ commutative\ property\ a\cdot b=b\cdot a; \ \ \ \ \ \ a+b=b+a\\\\=2p^{1+2}-(2\cdot4)p^{1+1}-(2\cdot7)p+3p^2-(3\cdot4)p-21\\\\=2p^3-8p^2-14p+3p^2-12p-21\\\\=2p^3+(-8p^2+3p^2)+(-14p-12p)-21\\\\=\boxed{2p^3-5p^2-26p-21}\)
