Question

# What is the fourth term of (x – 5y)^{96}?

- 125
^{96}C_{3} x^{93} y^{3} - 625
^{96}C_{3} x^{93} y^{4} - 625
^{96}C_{4} x^{92} y^{4} - 125
^{96}C_{4} x^{92} y^{4}

^{96}C_{3}x^{93}y^{3}^{96}C_{3}x^{93}y^{4}^{96}C_{4}x^{92}y^{4}^{96}C_{4}x^{92}y^{4}Hint:

### Use the bionimal formula for the 4th term to find the forth term.

## The correct answer is: 125 ^{96}C_{3} x^{93} y^{3}

STEP BY STEP SOLUTION

T_{r + 1} = ^{n}C_{r} x^{n – r} y^{r}

Here, the first term is 4, and the second term is 5y.

n = 96

r = 3

Therefore, T_{r + 1} = ^{96}C_{3} x^{96 – 3} (5y)^{3}

= 125 ^{96}C_{3} x^{93} y^{3}

_{r + 1}=

^{n}C

_{r}x

^{n – r}y

^{r}

Therefore, T

_{r + 1}=

^{96}C

_{3}x

^{96 – 3}(5y)

^{3}

^{96}C

_{3}x

^{93}y

^{3}

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