Answer :
Question:
Iliana multiplied 3p – 7 and 2p^2 – 3p – 4. Her work is shown in the table.
Which is the product?
6p^3 + 23p^2 + 9p + 28
6p^3 – 23p^2 – 9p + 28
6p^3 – 23p^2 + 9p + 28
6p^3 + 23p^2 – 9p + 28
Answer:
Option C: [tex]6 p^{3}-23 p^{2}+9 p+28[/tex] is the correct answer.
Explanation:
The two expressions are [tex]3 p-7[/tex] and [tex]\left2 p^{2}-3 p-4\right[/tex]
The product of the expression can be determined by multiplying each of the first term with the second term of the expression, we get,
[tex](3 p-7)\left(2 p^{2}-3 p-4\right)[/tex]
[tex]3 p \cdot 2 p^{2}+3 p(-3 p)+3 p(-4)+(-7) \cdot 2 p^{2}+(-7)(-3 p)+(-7)(-4)[/tex]
Simplifying we have,
[tex]6p^3-9p^2-12p-14p^2+21p+28[/tex]
Adding the like terms, we have,
[tex]6 p^{3}-23 p^{2}+9 p+28[/tex]
Thus, the product of the two expression is [tex]6 p^{3}-23 p^{2}+9 p+28[/tex]
Hence, Option C is the correct answer.