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द्विपद प्रमेय का प्रयोग करके निम्न का विस्तार कीजिए - (i) ` ( ( 2x ) /( 3 ) - ( 3 )/( 2x))^ 6 ` (ii) ` ( 2x - (3 ) /( y ) ) ^ 5 ` (iii) ` ( 1 - x + x ^ 2 ) ^ 4 ` (iv) ` ( 1 + x + x ^ 2 ) ^ 3 ` (v) ` (sqrtx + sqrty ) ^( 10 ) ` (vi ) ` (3sqrt x- 3 sqrt y ) ^ 6 ` |
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Answer» (i) ` ( 64 x ^ 6 ) /( 729 ) - ( 32 x ^ 4 ) /( 27 ) + ( 20 x ^ 2) /( 3 ) - 20 + ( 135 ) /( 4 x ^ 2 ) - ( 243 ) /( 8 x ^ 4 ) + ( 729 ) /( 64 x ^ 6 ) `, (ii) ` 32x ^5 - ( 240 x^ 4 ) /( y ) + ( 720 x^ 3 )/( y^ 2 ) - (1080 x^ 2) /( y ^ 3 ) + ( 810 x ) /( y ^ 4 ) - ( 243 ) /( y ^ 5 ) ` (iii) ` 1- 4x + 10 x ^ 2 - 16 x^ 3 + 19 x ^ 4 - 16 x^ 5 + 10 x ^ 6 - 4x ^ 7 + x ^ 8 ` (iv) ` 1 + 3x + 6x ^ 2 + 7 x ^ 3 + 6 x ^ 4 + 3x ^ 5 + x ^ 6 ` (v) ` x ^ 5 + 10 x ^ ( 9//2) y ^ ( 1//2) + 45 x ^4 y + 120 x ^ ( 7//2 ) y ^ ( 3//2 ) + 210 x ^ 3 y ^ 2 + 252 x ^ (5//2) y ^ ( 5//2 ) + 210 x ^ 2 y ^ 3 + 120 x ^ ( 3//2 ) y ^ ( 7//2) + 45 x y ^ 4 + 10 x ^ ( 1//2) y^ ( 9//2) + y ^ 5 ` (vi) ` x ^ 2 - 6 x ^ ( 5//3) y ^ ( 1// 3) + 15 x ^( 4//3 ) y ^ ( 2//3) - 20 xy + 15 x^( 2//3) y ^( 4//3) - 6x ^( 1//3) y ^ ( 5//3) + y ^ 2 ` |
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