Expand (2x + 3)^5 using the Binomial Theorem and Pascal’s triangle. Show all steps.
1 answer:
Answer:
32x⁵ + 240x⁴ + 720x³ + 1080x² + 810x + 243
Step-by-step explanation:
(2x + 3)⁵
₅C₀ (2x)⁵ (3)⁰ + ₅C₁ (2x)⁴ (3)¹ + ₅C₂ (2x)³ (3)² + ₅C₃ (2x)² (3)³ + ₅C₄ (2x)¹ (3)⁴ + ₅C₅ (2x)⁰ (3)⁵
Use Pascal's triangle to find nCr.
1 (2x)⁵ (3)⁰ + 5 (2x)⁴ (3)¹ + 10 (2x)³ (3)² + 10 (2x)² (3)³ + 5 (2x)¹ (3)⁴ + 1 (2x)⁰ (3)⁵
(2x)⁵ + 15 (2x)⁴ + 90 (2x)³ + 270 (2x)² + 405 (2x)¹ + 243
32x⁵ + 240x⁴ + 720x³ + 1080x² + 810x + 243
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Answer: Simple interest rate = 3%.
Step-by-step explanation: We are given invested amount = $5000.
Number of years of investment = 4 years.
Interest earned = $600.
Simple interest formula.
I = P R T.
Where I is the earned interest, P is the invested amount , R is the rate of interest and T is the time in years.
Plugging values in formula, we get
600 = 5000 × R × 4
600 = 20000R.
Dividing both sides by 20000, we get
0.03 = R.
Multiplying by 100 to convert it in percentage, we get
0.03 × 100 = R
R = 3 %.