7. Use Pascal's Triangle to expand the binomial (2x + 2)¹. O 16x¹64x³ +96x² - 64x + 16 - 16x4 + 64x³ +96x²64x - 16 O 16x¹-64x³ - 96x² + 64x 16 1 O 16x¹ +64x³ +96x² + 64x + 16
7. Use Pascal's Triangle to expand the binomial (2x + 2)¹. O 16x¹64x³ +96x² - 64x + 16 - 16x4 + 64x³ +96x²64x - 16 O 16x¹-64x³ - 96x² + 64x 16 1 O 16x¹ +64x³ +96x² + 64x + 16
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
Related questions
Question
![**Question 7: Use Pascal's Triangle to Expand the Binomial (2x + 2)^4**
Choose the correct expanded form from the options below:
- Option A: \(16x^4 - 64x^3 + 96x^2 - 64x + 16\)
- Option B: \(16x^4 + 64x^3 + 96x^2 - 64x - 16\)
- Option C: \(16x^4 - 64x^3 - 96x^2 + 64x - 16\)
- Option D: \(16x^4 + 64x^3 + 96x^2 + 64x + 16\)
**Explanation of Pascal's Triangle:**
Pascal's Triangle is a triangular array of binomial coefficients. The coefficients correspond to the elements in the expansion of a binomial expression of the form \((a + b)^n\). For \((2x + 2)^4\), we use the fifth row of Pascal's Triangle, which is:
1, 4, 6, 4, 1
These coefficients multiply the terms in the expansion:
\[ (2x + 2)^4 = \sum_{k=0}^{4} \binom{4}{k} (2x)^{4-k} (2)^k \]
The expansion based on the coefficients and applying the binomial theorem is:
\[ = 1 \cdot (2x)^4 + 4 \cdot (2x)^3 \cdot (2) + 6 \cdot (2x)^2 \cdot (2)^2 + 4 \cdot (2x) \cdot (2)^3 + 1 \cdot (2)^4 \]
\[ = 16x^4 + 64x^3 + 96x^2 + 64x + 16 \]
Thus, the correct option is:
- Option D: \(16x^4 + 64x^3 + 96x^2 + 64x + 16\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F050b7896-96e1-4a53-ae28-da4cd34956eb%2F07883149-6ed4-4220-9bbd-0f163ca731e3%2Fzvfy6op_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 7: Use Pascal's Triangle to Expand the Binomial (2x + 2)^4**
Choose the correct expanded form from the options below:
- Option A: \(16x^4 - 64x^3 + 96x^2 - 64x + 16\)
- Option B: \(16x^4 + 64x^3 + 96x^2 - 64x - 16\)
- Option C: \(16x^4 - 64x^3 - 96x^2 + 64x - 16\)
- Option D: \(16x^4 + 64x^3 + 96x^2 + 64x + 16\)
**Explanation of Pascal's Triangle:**
Pascal's Triangle is a triangular array of binomial coefficients. The coefficients correspond to the elements in the expansion of a binomial expression of the form \((a + b)^n\). For \((2x + 2)^4\), we use the fifth row of Pascal's Triangle, which is:
1, 4, 6, 4, 1
These coefficients multiply the terms in the expansion:
\[ (2x + 2)^4 = \sum_{k=0}^{4} \binom{4}{k} (2x)^{4-k} (2)^k \]
The expansion based on the coefficients and applying the binomial theorem is:
\[ = 1 \cdot (2x)^4 + 4 \cdot (2x)^3 \cdot (2) + 6 \cdot (2x)^2 \cdot (2)^2 + 4 \cdot (2x) \cdot (2)^3 + 1 \cdot (2)^4 \]
\[ = 16x^4 + 64x^3 + 96x^2 + 64x + 16 \]
Thus, the correct option is:
- Option D: \(16x^4 + 64x^3 + 96x^2 + 64x + 16\)
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