Question

Iliana multiplied 3p – 7 and 2p2 – 3p – 4. Her work is shown in the table.

The expression (3 p minus 7)(2 p squared minus 3 p minus 4) is shown above a table with 3 columns and 2 rows. First column is labeled 2 p squared, second column is labeled negative 3 p, the third column is labeled negative 4. First row is labeled 3 p with entries 6 p cubed, negative 9 p squared, negative 12 p. Second row is labeled negative 7 with entries negative 14 p squared, 21 p, 28.
Which is the product?

6p3 + 23p2 + 9p + 28
6p3 – 23p2 – 9p + 28
6p3 – 23p2 + 9p + 28
6p3 + 23p2 – 9p + 28

Answer 1

Answer:

Option C is correct.

$(3p - 7)(2 {p}^{2} - 3p - 4)= 6 {p}^{3} - 23 {p}^{2} + 9p + 28$

Step-by-step explanation:

To find the product of given expression

$(3p - 7)(2 {p}^{2} - 3p - 4) \\ \\ = 3p(2 {p}^{2} - 3p - 4) - 7(2 {p}^{2} - 3p - 4) \\ \\ = 6 {p}^{3} - 9 {p}^{2} - 12p - 14 {p}^{2} + 21p + 28 \\ \\ = 6 {p}^{3} - 9 {p}^{2} - 14 {p}^{2} - 12p + 21p + 28 \\ \\ = 6 {p}^{3} - 23 {p}^{2} + 9p + 28$

Hope it helps you.