Find the product of (4x10+9x7)(−4x10−9x7)

Question

(
4
𝑥
10
+
9
𝑥
7
)
(
−
4
𝑥
10
−
9
𝑥
7
)
.(1 point)
Responses

−16x20−81x14
−
16
𝑥
20
−
81
𝑥
14
negative 16 x to the 20th power minus 81 x to the 14th power

16x20−72x17+81x14
16
𝑥
20
−
72
𝑥
17
+
81
𝑥
14
16 x to the 20th power minus 72 x to the 17th power plus 81 x to the 14th power

−16x100−72x70−81x49
−
16
𝑥
100
−
72
𝑥
70
−
81
𝑥
49
negative 16 x to the 100th power minus 72 x to the 70th power minus 81 x to the 49th power

−16x20−72x17−81x14

Answer 1

To find the product \((4x^{10} + 9x^7)(-4x^{10} - 9x^7)\), we can use the distributive property (also known as the FOIL method for binomials).

Let's compute the product step by step:

\[ (4x^{10} + 9x^7)(-4x^{10} - 9x^7) \]

1. First, we'll distribute \(4x^{10}\):

   • \(4x^{10} \cdot (-4x^{10}) = -16x^{20}\)
   • \(4x^{10} \cdot (-9x^7) = -36x^{17}\)

2. Next, we'll distribute \(9x^7\):

   • \(9x^7 \cdot (-4x^{10}) = -36x^{17}\) (because the term is the same as above)
   • \(9x^7 \cdot (-9x^7) = -81x^{14}\)

Now, we add all of these results together:

\[ -16x^{20} - 36x^{17} - 36x^{17} - 81x^{14} \]

Combine the like terms for \(x^{17}\):

\[ -16x^{20} - 72x^{17} - 81x^{14} \]

Thus, the product is:

\[ -16x^{20} - 72x^{17} - 81x^{14} \]

Therefore, the correct response is:

\(-16x^{20} - 72x^{17} - 81x^{14}\)