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# give shortcut to this question . what is the coefficient of x^5 in  ( 1+ 2x)^6 * (1 - x)^7

Neer Varshney
76 Points
10 years ago

Do not open this expression fully just consider only those in which u think power will come five.

Do a little bit of thinking in ur minds first like:

(1+2x)^6 * (1-x)^7

= (1+2x)^3(^2) * (1-x)7.

Then in the next step dont write the powers in which there is  no power 5.

jagdish singh singh
173 Points
10 years ago

$(1+2x)^6 =\\\\ \binom{6}{0}+\binom{6}{1}.2x+\binom{6}{2}.4x^2+\binom{6}{3}.8x^3+\binom{6}{4}.16x^4+\binom{6}{5}.32x^5+\binom{6}{6}.64x^6..............(1)\\\\\\\\ (1-x)^7=\\\\ \binom{7}{0}-\binom{7}{1}.x+\binom{7}{2}.x^2-\binom{7}{3}.x^3+\binom{7}{4}.x^4-\binom{7}{5}.x^5+\binom{7}{6}.x^6-\binom{7}{7}.x^7................(2)\\\\ Now Multiply ..(1) and ..(2),We Get...\\\\ And find Coeff. of x^5$