Lionfish5
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Please help. Real answers please.

What is the 4th term of the expansion (1-2x)^n if the binomial coefficients are taken from the row of Pascal's triangle shown here?

1 6 15 20 15 6 1

A. -160x^3
B. 160x^3
C. 240x^4
D. -20x^3

Respuesta :

Answer:

-160x³

Step-by-step explanation:

4th term: n = terms - 1 = 4-1 = 3

1*1⁶*(-2x)⁰ + 6*1⁵*(-2x)¹ + 15*1⁴*(-2x)² +20*1³*(-2x)³ + 15*1²*(-2x)⁴ + ..........

                                                                 ↑

                                                             4th term

20*1³*(-2x)³ = 20*(-8x³) = -160x³

The fourth term of the expansion of (1 - 2x)ⁿ is; A;  -160x³

Binomial Expansion Theorem

We want to find the fourth term of the expansion given as;

(1 - 2x)ⁿ

Using binomial coefficients, the first 7 coefficients are;

1 6 15 20 15 6 1

Now, using the binomial expansion method, we have;

(1 - 2x)⁶ = (1 × 1⁶ × (-2x)⁰) + (6 ×1⁵ × (-2x)¹) + (15 × 1⁴ × (-2x)²) + (20 × 1³ × (-2x)³) + (15 × 1² × (-2x)⁴) + .......

Looking at the expansion, the fourth term is identified as; (20 × 1³ × (-2x)³)

Simplifying that gives; -160x³

Read more about Binomial Expansion at; https://brainly.com/question/13602562

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