The fourth term in the expansion (x - 2y)^ 12 is: - Vidyadip

MCQ

The fourth term in the expansion $(x - 2y)^{12}$ is:

A
$ -1670 x^9 \times y^3 $
B
$ -7160 x^9 \times y^3 $
✓
$ -1760 x^9 \times y^3 $
D
$ -1607 x^9 \times y^3 $

✓

Answer

Correct option: C.

$ -1760 x^9 \times y^3 $

$4^{th}$ term in $(x-2 y)^{12}=T_4$
$ =T_3+1 $
$ ={ }^{12} C_3(x)^{12-3} \times(-2 y)^3$
$={ }^{12} C_3 x^9 \times\left(-8 y^3\right)$
$ = {\frac{(12 \times 11 \times 10)}{(3 \times 2 \times 1)} \times \text{x}^9 \times (-8\text{y}^³)}$
$= - (2 \times 11 \times 10 \times 8) \times x^9\times y^3$
$= -1760 x^9\times y^3$

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