Math, asked by aryan674232, 10 months ago

Find the term in the expansion of (2x-5)^6 which have 1.greatest binomial coefficient, 2.greatest numerical coefficient, 3. Algebraically greatest coefficient & 4. Algebraically least coefficient.​

Answers

Answered by KrystaCort
12

Answer:

The expansion of:

(2x - 5)⁶ = ⁶C₀ (2x)⁶ + ⁶C₁ (2x)⁵(-5) + ⁶C₁ (2x)⁵(-5) + ⁶C₂ (2x)⁴(-5)² + ⁶C₃ (2x)³(-5)³ + ⁶C₄ (2x)²(-5)⁴ + ⁶C₅ (2x)(-5)⁵ + ⁶C₆ (-5)⁶

1. greatest binomial coefficient: ⁶C₀ (2x)⁶

2. greatest numerical coefficient:  ⁶C₃ (2x)³(-5)³ and ⁶C₄ (2x)²(-5)⁴

3. Algebraically greatest coefficient:  ⁶C₄ (2x)²(-5)⁴

4. Algebraically least coefficient: ⁶C₀ (2x)⁶

Answered by assalterente
11

Answer:

Step-by-step explanation:

Our aim is to find the term in the expansion of (2x-5)^6 which have the given properties.

Our first line asks for a greatest binomial coefficient. Hence, since we have to find the term in expansion of (2x-5)^6 we have the following expansion of the term:

(2x - 5)⁶ = ⁶C₀ (2x)⁶ + ⁶C₁ (2x)⁵(-5) + ⁶C₁ (2x)⁵(-5) + ⁶C₂ (2x)⁴(-5)² + ⁶C₃ (2x)³(-5)³ + ⁶C₄ (2x)²(-5)⁴ + ⁶C₅ (2x)(-5)⁵ + ⁶C₆ (-5)⁶

Now, in order to compute all lines we get that for the first question, the greatest binomial coefficient is ⁶C₀ (2x)⁶.

In the second line, the greatest numerical coefficient are ⁶C₃ (2x)³(-5)³ and ⁶C₄ (2x)²(-5)⁴.

Third question, our algebraically greatest coefficient is ⁶C₄ (2x)²(-5)⁴.

At last but not least, the algebraically least coefficient is equal to ⁶C₀ (2x)⁶.

I hope this helps your studies!! Keep it up!!

Similar questions