Coefficient of x4 in the expansion of 1(x+1)(x+2) is
A
132
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B
1132
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C
2132
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D
3132
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Solution
The correct option is D3132 Given, 1(x+1)(x+2) =x+2−(x+1)(x+1)(x+2) =1x+1−1x+2 =(1+x)−1−(2+x)−1 =(1+x)−1−12(1+x2)−1 Hence coefficient of x4 will be n(n−1)(n−2)(n−3)4!−12n(n−1)(n−2)(n−3)4!124 =−1(−2)(−3)(−4)4!−125−1(−2)(−3)(−4)4! =4!4!−1324!4! =1−132 =3132