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Question
Expand (3x2 + 2y)5
Solution
Here a = 3x2 , b = 2y, n = 5
Using binomial theorem,
(3x2 + 2y)5 = 5C0 (3x2)5 (2y)0 + 5C1 (3x2)4 (2y)1 + 5C2 (3x2)3 (2y)2 + 5C3 (3x2)2 (2y)3 + 5C4 (3x2)1 (2y)4 + 5C5 (3x2)0 (2y)5
Since, 5C0 = 5C5 = 1, 5C1 = 5C4 = 5,
5C2 = 5C3 = `(5 xx 4)/(2 xx 1)` = 10
∴ (3x2 + 2y)5 = 1(243.x10)(1) + 5(81x8) (2y) + 10(27x6).(4y2) + 10.(9x4) (8y3) + 5(3x2) (16y4) + 1(1)(32y5)
= 243x10 + 810x8y + 1080x6y2 + 720x4y3 + 240x2y4 + 32y5
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