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Answer :
To find the expression equivalent to [tex]\((4x^5 + 11)^2\)[/tex], let's break down the problem and use the information given to identify the correct expression.
1. Original Expression: We are given [tex]\((4x^5 + 11)^2\)[/tex].
2. Expanding the Expression: We know that when you square a binomial, [tex]\((a + b)^2\)[/tex], the formula is [tex]\(a^2 + 2ab + b^2\)[/tex].
Applying this formula:
- [tex]\(a = 4x^5\)[/tex] and [tex]\(b = 11\)[/tex]
- [tex]\(a^2 = (4x^5)^2 = 16x^{10}\)[/tex]
- [tex]\(2ab = 2 \cdot 4x^5 \cdot 11 = 88x^5\)[/tex]
- [tex]\(b^2 = 11^2 = 121\)[/tex]
3. Combine These Together:
[tex]\[
(4x^5 + 11)^2 = 16x^{10} + 88x^5 + 121
\][/tex]
4. Matching with the Options: We need to see which of the options matches this expanded form:
- [tex]\(16x^5 + 121\)[/tex]
- [tex]\(16x^{40} + 121\)[/tex]
- [tex]\(16x^{10} + 38x^5 + 12\)[/tex]
- [tex]\(16x^{25} + 35x^8 + 1221\)[/tex]
5. Correct Expression: The expanded form, [tex]\(16x^{10} + 88x^5 + 121\)[/tex], doesn't match any of the provided options. Therefore, none of the given options are equivalent to the expanded expression.
Keep in mind, it happens that answer choices given sometimes do not include the correct answer, and that's okay. In this case, it's a good learning point to verify calculations and understand that the expansion of a binomial can yield unexpected choices not provided in a list.
1. Original Expression: We are given [tex]\((4x^5 + 11)^2\)[/tex].
2. Expanding the Expression: We know that when you square a binomial, [tex]\((a + b)^2\)[/tex], the formula is [tex]\(a^2 + 2ab + b^2\)[/tex].
Applying this formula:
- [tex]\(a = 4x^5\)[/tex] and [tex]\(b = 11\)[/tex]
- [tex]\(a^2 = (4x^5)^2 = 16x^{10}\)[/tex]
- [tex]\(2ab = 2 \cdot 4x^5 \cdot 11 = 88x^5\)[/tex]
- [tex]\(b^2 = 11^2 = 121\)[/tex]
3. Combine These Together:
[tex]\[
(4x^5 + 11)^2 = 16x^{10} + 88x^5 + 121
\][/tex]
4. Matching with the Options: We need to see which of the options matches this expanded form:
- [tex]\(16x^5 + 121\)[/tex]
- [tex]\(16x^{40} + 121\)[/tex]
- [tex]\(16x^{10} + 38x^5 + 12\)[/tex]
- [tex]\(16x^{25} + 35x^8 + 1221\)[/tex]
5. Correct Expression: The expanded form, [tex]\(16x^{10} + 88x^5 + 121\)[/tex], doesn't match any of the provided options. Therefore, none of the given options are equivalent to the expanded expression.
Keep in mind, it happens that answer choices given sometimes do not include the correct answer, and that's okay. In this case, it's a good learning point to verify calculations and understand that the expansion of a binomial can yield unexpected choices not provided in a list.
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