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Home  >>  CBSE XI  >>  Math  >>  Binomial Theorem
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Expand each of the expressions:$(2x-3)^6$

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  • $(a-b)^n=nC_0a^n-nC_1a^{n-1}b+nC_2a^{n-2}b^2.......+(-1)^nnC_ra^{n-r}b^r+......nC_n(-b)^n$
$(2x-3)^6=6C_0(2x)^6+6C_1(2x)^5(-3)+6C_2(2x)^4(-3)^2+6C_3(2x)^3(-3)^3+6C_4(2x)^2(-3)^4+6C_5(2x)(-3)^5+6C_6(2x)^0(-3)^6$
$\Rightarrow 64x^6+\large\frac{6}{1}$$x(32 x^5)(-3)+\large\frac{6.5}{1.2}$$(16x^4).9+\large\frac{6.5.4}{1.2.3}$$(8x^3)(-27)+\large\frac{6.5}{1.2}$$(4x^2)(81)+\large\frac{6}{1}$$(2x)(-243)+729$
$\Rightarrow 64x^6-576x^5+2160x^4-4320x^3+4860x^2-2916x+729$
answered Jun 20, 2014 by sreemathi.v
 
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