Answer :
To solve the problem of multiplying [tex]\((5 - 4x^3)(5 + 4x^3)\)[/tex], we can use the identity known as the difference of squares. This identity tells us that:
[tex]\[
(a - b)(a + b) = a^2 - b^2
\][/tex]
In this case, we can identify [tex]\(a\)[/tex] and [tex]\(b\)[/tex] as follows:
- [tex]\(a = 5\)[/tex]
- [tex]\(b = 4x^3\)[/tex]
Using the difference of squares identity, we substitute these values in:
[tex]\[
(5 - 4x^3)(5 + 4x^3) = 5^2 - (4x^3)^2
\][/tex]
Now let's calculate step-by-step:
1. Calculate [tex]\(5^2\)[/tex]:
[tex]\[
5^2 = 25
\][/tex]
2. Calculate [tex]\((4x^3)^2\)[/tex]:
[tex]\[
(4x^3)^2 = 16x^6
\][/tex]
Now, apply the identity:
[tex]\[
25 - 16x^6
\][/tex]
The expression simplifies to the term:
[tex]\[
25 - 16x^6
\][/tex]
So, the correct answer is:
D [tex]\(25 - 16x^6\)[/tex]
[tex]\[
(a - b)(a + b) = a^2 - b^2
\][/tex]
In this case, we can identify [tex]\(a\)[/tex] and [tex]\(b\)[/tex] as follows:
- [tex]\(a = 5\)[/tex]
- [tex]\(b = 4x^3\)[/tex]
Using the difference of squares identity, we substitute these values in:
[tex]\[
(5 - 4x^3)(5 + 4x^3) = 5^2 - (4x^3)^2
\][/tex]
Now let's calculate step-by-step:
1. Calculate [tex]\(5^2\)[/tex]:
[tex]\[
5^2 = 25
\][/tex]
2. Calculate [tex]\((4x^3)^2\)[/tex]:
[tex]\[
(4x^3)^2 = 16x^6
\][/tex]
Now, apply the identity:
[tex]\[
25 - 16x^6
\][/tex]
The expression simplifies to the term:
[tex]\[
25 - 16x^6
\][/tex]
So, the correct answer is:
D [tex]\(25 - 16x^6\)[/tex]
